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Local Direct Elections, Local Information and Meritocratic Selection1

Yu Wang and Renfu Luo

Job Market Paper

(September 29, 2019)

Abstract

This paper studies the relationship and mechanism between local direct elections in rural China and meritocratic selection. Our theoretical model upon Bayesian framework demonstrates that local direct elections facilitate the fulfillment of the meritocratic selection both for village leaders and for village party secretaries. As local direct elections empower the selection for village leaders to village residents, who naturally communicate of more times with village leader candidates than township officials, the representative village resident infers candidates’ virtue and capacity of higher accuracy and precision. Therefore, the introduction of local direct elections improves village leaders’ mean values of composite virtue-and-capacity and reduces their variances of composite virtue-and-capacity. Further, since village leaders are the major candidates for village party secretaries, village party secretaries’ mean values of composite virtue-and-capacity are also improved. Using quality of village roads, we find supportive empirical evidence for our theoretical demonstrations. Keywords: Local Direct Election, Local Information, Meritocratic Selection

���������������������������������������� ����1 Wang: Department of Applied Economics, University of Minnesota (email: wang5979@umn.edu); Luo:

China Center for Agricultural Policies, Peking University (email: luorf.ccap@pku.edu.cn). We thank Marc

Bellemare, Loren Brandt, Jay Coggins, Paul Glewwe, John Freeman and Sean Sylvia for valuable

comments and suggestions. All errors are authors.

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“When the Grand course was pursued, a public and common spirit ruled all under the sky; they chose men of talents, virtue, and ability; their words were sincere, and what they cultivated was harmony.” – Confucius (450 B.C., translated by James Legge [1885]), Li Chi: Book of Rites “The aim of every political constitution, is or ought to be, first to obtain for rulers men who possess most wisdom to discern, and most virtue to pursue, the common good of society.” – Hamilton, Madison and Jay (1788 [2008]), The Federalist Papers

I. Introduction

Meritocratic selection is pursued all over the world, both ancient and modern

times. Dating back to around 500 B.C., Chinese politicians and philosophers

raised that those who governed should be selected by merit rather than inherited

status (Sienkewicz, 2003). As the concept of pursuing meritocracy spread to

Europe and the U.S., it was favored by philosophers (Kazin et al., 2010) and

claimed in political statements (Hamilton, Maddison and Jay, 2008).

China has evolved a series of top-down political selection schemes, of which

the mechanism emphasizes the assessment, recommend and promotion for

politicians upon their virtue and capacity, aiming at meritocratic selection. In

around 134 B.C., the assessment & recommend system targeting noble families

was established (Qian, 2012). By enlarging the enfranchisement, the civil exam

system targeting scholars was developed in around 605 A.D., prevailed for over

1000 years, and has greatly influenced political selection schemes in China and

other countries (Elman, 2013; Bai and Jia, 2016; Bell, 2016).

Unlike top-down schemes in China, electoral system, the bottom-up political

selection scheme, was established in ancient Western regimes and prevailed

gradually. Since around 508 B.C., Athenian democracy was established; by

enlarging the enfranchisement, the electoral system has evolved to modern

representative democracy (Loeper, 2017). The mechanism of election

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emphasizes the incentives for politicians upon their behaviors, aiming at the ex

post accountability (Laffont, 2000; Besley, 2005).

The introduction of local direct elections to Chinese top-down political

selection system enables us to identify the relationship and mechanism between

local direct elections and meritocratic selection. We build up a theoretical model,

demonstrating that local direct elections in rural China, by providing local

information on village leader candidates’ virtue and capacity, facilitate the

fulfillment of meritocratic selection for village leaders. Even if the political

selection scheme for village party secretaries remains top-down, local direct

elections for village leaders also facilitate the fulfillment of meritocratic

selection for village party secretaries. Using quality of over 550 village roads,

our empirical evidence supports our theoretical predictions2.

Unlike previous studies regarding elections basically as ex post incentives for

politicians and using the game theory framework3, our model uses the Bayesian

framework to explain how local direct elections, by providing local information,

facilitate the fulfillment of meritocratic selection for village leaders. The

introduction of local direct elections empowers the selection for village leaders

to village residents from township officials. Village residents naturally

communicate with village leader candidates of more times than township

officials, implying village residents’ advantage in local information on

candidates (Ghatak, 1999; Bell, 2016). Therefore, the representative village

resident infers village leader candidates’ virtue and capacity of higher accuracy

and precision than the representative township official. Our theoretical model

���������������������������������������� ����2 Our theoretical findings are empirically supported by this paper and Wong et al., (2017), which also

provides motivations for this paper’s theoretical reasoning.�3 See Laffont (2000) and Besley (2006) for theoretical demonstrations, Ferraz and Finan (2011) and De

Janvry et al. (2012) for empirical evidence and Bell (2016) for demonstrations in political science.

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proves, with the inference of higher accuracy, that in a representative village,

the mean value of the elected village leader’s composite virtue-and-capacity (a

weighted average of virtue and capacity) exceeds that of the appointed village

leader’s. It also proves, with the inference of higher precision, that the variance

of the elected village leader’s composite virtue-and-capacity is smaller that of

the appointed village leader’s. These theoretical findings are in line with Hayek

(1945) and Chan (2013) that assessment and decisions must be left to people

with advantages in local information.

Due to the local information on village leader candidates’ virtue and capacity

that local direct elections provide in selecting village leaders, our model

demonstrates that local direct elections further facilitates the fulfillment of

meritocratic selection for village party secretaries. Village leaders are major

candidates of village party secretaries (O'brien and Li, 2000), and the

performance-based promotion for them as village party secretaries is both the

ex post assessment and the ex ante selection for village party secretaries. Our

model shows that because the mean value of the elected village leader’s

composite virtue-and-capacity exceeds that of the appointed one’s, the elected

village leader’s promotion likelihood surpasses the appointed one’s. It further

shows that the introduction of local direct elections raises the village party

secretary’s composite virtue-and-capacity. Therefore, the performance-based

promotion for village party secretaries not only holds village leaders

accountable, integrated with local direct elections that provide local information,

it is also endowed with meritocratic selection.

The rest of this paper is organized as follows: Section II introduces the

institutional backgrounds. Section III develops the theory. Section IV discusses

the empirical strategies and presents the empirical results. Section V concludes.

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II. Local Governance in Rural China

� � The Chinese village administrative organizations consist of village

committees, the de facto government entities at the village level, chaired by

village leaders, and the village-leveled leadership of the Chinese Communist

Party (CCP) named village party branches, chaired by village party secretaries.

Village party branches supervise village committees, and thus village party

secretaries are higher than village leaders in Chinese bureaucratic hierarchy,

stipulated by the “Organic Law of the Village Committees (OLVC)” (National

People’s Congress of China, 1998) and the “Working Regulation on the Rural

Grassroots Organizations of Chinese Communist Party (WRRGOCCP)”

(Central Committee of the Chinese Communist Party, 1999). Village leaders’

major responsibility is providing village public infrastructure and service,

developing the local economy, and improve village residents’ income (OLVC,

1998; Martinez-Bravo et al., 2011); yet village party secretaries’ duty in

developing the local economy is approving village leaders’ plans and

monitoring the implementation (WRRGOCCP, 1999; Oi and Rozelle, 2000).

The selection scheme for village leaders has transited from appointments by

township officials to local direct elections by village residents. The introduction

of local direct elections in rural China has experienced a gradual process4

(Martinez-Bravo et al., 2014). Until 2010, most villages in rural China have

���������������������������������������� ����4 In 1998, the National People’s Congress of China passed the revised “Organic Law of the Village

Committees (OLVC)”, introducing local direct elections for village leaders in rural China, which brought

elections for village leaders with open nomination, competitive election (O’Brien and Han, 2009). After

the national legislation in 1998, each province in China, in the following years, introduced its own

“Provincial Measures for Implementing the Organic Law of Village Committees” to provide further

instructions on the implementation of local direct elections (O’Brien and Zhao, 2011). Counties and

townships then followed suit (Wong et al., 2017).

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introduced local direct elections (Padró i Miquel et al., 2015; Wong et al., 2017).

Both appointments and local direct elections emphasize meritocratic selection,

requiring that village leader candidates be law-abiding, of moral integrity and

be intrinsically willing to serve village residents; and be of some diploma and

administrative capacity (OLVC, 1998). Village leader candidates are then

selected by village residents or township officials for village leaders with the

likelihood of being selected positively associated with their virtue and capacity

(Bell, 2016; Tang, 2016), rooted in the concept and practice of meritocratic

selection in Chinese history (Zhang, 2012).

Village party secretaries are appointed by township officials, which also

emphasizes meritocratic selection regarding village party secretary candidates’

virtue and capacity. WRRGOCCP (1999) and its following versions, regulated

the procedures of selecting village party secretaries and stipulated the decisive

role of township officials in this selection5. This working regulation requires

that village party secretaries be qualified in professional knowledge and

working skills, be responsive to village residents’ needs and demands, and be

intrinsically motived to serve village residents. Village leaders are the major

candidates for village party secretaries (O'brien and Li, 2000).

III. Theory

Our theoretical model upon Bayesian framework discusses how the

introduction of local direct elections to a representative village facilitates the

���������������������������������������� ����5 Township party officials basically have the following ways to select for village party secretaries. (1)

Village party secretaries are directly appointed by township party officials. (2) Village party branch

committee members are firstly elected by village party members, then village party secretaries are

appointed by township party officials or elected among those committee members and finally approved

by township party officials. (3) Village party secretary candidates are firstly nominated by township party

officials, then elected village party members to serve as village party secretaries.

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fulfillment of the meritocratic selection both for the village leader and for the

village party secretary6.

A. Inferences with Village Leader Candidates

In this section, we use the Bayesian framework to discuss the inference of

village leader candidates’ virtue and capacity in a representative village. We find

that because the representative village resident naturally communicates with

village leader candidates of more times than the representative township official

does, the representative village resident infers village leader candidates’ virtue

and capacity of higher accuracy and precision.

1. Setup: Our theory discusses a representative village, in which all adult

village residents are potential village leader candidates. Each one has two

personal characteristics: virtue and capacity, both are assumed to be

independent and identically distributed over [0, 1] with both means of 0.57.

After the local direct election is introduced to this representative village, a

pool of village leader candidates, subset of all the potential candidates,

competes for being elected as the village leader by village residents. Before this

introduction, a pool of village leader candidates competes for being appointed

as the village leader by township officials. Village leader candidates’ virtue is

denoted as &', with &' ∈ 0,1 , and their capacity is denoted as )', with )' ∈

���������������������������������������� ����6 According to our survey data, around 86% (1718 out of 2000) interviewed village residents replied that

local direct elections were implemented law-abidingly, in which no corruption or conspiracy exists. 7 Village residents’ virtue and capacity are both assumed to be bounded, because (1) the number of

residents in a village is usually small (Liu et al., 2009; Martinez-Bravo et al. 2014), and (2) their

socioeconomic characteristics, thinking patterns and behaviors, tend to be homogenous, due to the

homogenous socioeconomic, cultural and institutional constraints, as well as the long-term, generation-

by-generation interactions (Bell, 2016). For simplicity, we assume village residents’ virtue and capacity

are both bounded at [0, 1].

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0,1 , where * = {1,2, … } . In the following analysis, we discuss the

representative village resident instead of village residents, by assuming

homogenous perception among village residents over village leader candidates’

virtue and capacity, as well as the representative township official instead of

township officials, by assuming homogenous perception among township

officials over village leader candidates’ virtue and capacity.

2. Bayesian Inferences: Neither the representative village resident nor

township official observes each village leader candidate’s virtue or capacity. To

infer village leader candidates’ virtue and capacity, the representative village

resident or township official, by naturally communicating with each candidate,

obtains 0'12 , a series of observations of village leader candidate *’s virtue, in

the times of 3 = 1,… , 4567 and 1,… , 4899, respectively. 4567 represents the

ultimate times of natural communication between the representative village

resident and each village leader candidate, right before the representative village

resident makes the decision on which candidate to elect as the village leader.

4899 represents the ultimate times of natural communication between the

representative township official and each village leader candidate, right before

the representative township official makes the decision on which candidate to

appoint as the village leader. 0'12 is specified as,

(1) 0'12�&' + ;'1

where ;'1 is the series of random shocks in observing virtue. Similarly, the

representative village resident or township official, by naturally communicating

with each village leader candidate, obtains 0'1< , a series of observations of

village leader candidate * ’s capacity, in the times of 3 = 1,… , 4567 and

1,… , 4899, respectively. 0'1< is specified as,

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(2) 0'1<�)' + ='1

where ='1 is the series of random shocks in observing capacity.

Natural communication is defined to be the daily communication in work,

living or other circumstances, in which communicators behaves naturally and

artlessly (Bell, 2016). In addition, this communication induces no illegal

outcomes in village affairs management, like conspiracy or rent-seeking (Baker

and Faulkner, 1993), Since such communication happens in large number of

times and in various situations, communicators can hardly, and thus be basically

unwilling to, behave strategically to hide their real personally characteristics.

Therefore, it is acceptable to assume that first, the times of natural

communication are sufficiently large; second, the series of observations on

virtue or on capacity is normally distributed.

ASSUMPTION 1 (Natural communication and observations on virtue and

capacity): The representative village resident or township official communicates

with village leader candidates naturally, thus we have ;'1~?(0, ABCD ) and

='1~?(0, AFGD ) , and for a long time, thus we have 4567 and 4899 both

sufficiently large.

With ;'1~?(0, ABCD ),='1~?(0, AFG

D ), (1) and (2), we have 0'12~?(&', ABCD ),

and 0'1<~?()', AFGD ).

Before natural communication, both the representative village resident and

township official simply hold their prior perceptions over each village leader

candidate’s virtue and capacity. Assumption 2 discusses the distributions of

their prior perceptions.

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ASSUMPTION 2 (Prior distribution on village leader candidates’ virtue and

capacity): The representative village resident or township official’s prior

perceptions on village leader candidate *’s virtue are identically distributed as

? &'7, A2H

D , truncated at 0,1 , where &'7 ∈ [0, 1]. Their prior perceptions on

village leader candidate *’s capacity are identically distributed as ? )'7, A<H

D ,

truncated at 0,1 , where )'7 ∈ [0, 1]. &'7 and )'7, the prior means, and A2HD

and A<HD , the prior variance, are known to the representative village resident or

township official.

As both virtue and capacity are assumed to be bounded at [0, 1], and the

representative village resident or township official have long-term natural

communication with each village leader candidate, the representative village

resident or township official’s prior perception on each village leader

candidate’s virtue or capacity is truncated at 0,1 .

With the prior perception on virtue, and each time of natural communication,

the representative village resident or township official obtain the posteriorly

inferred perception of village leader candidates’ virtue. According to the Bayes’

Rule, such a posterior perception is obtained by iteration, such that the inferred

perception of virtue in period 3 is contingent on a previously inferred virtue,

the inferred perception virtue in period 3 − 1, and a posteriorly updated virtue,

the observation of virtue in in period 3.

Now we introduce deriving the density kernel of the posterior distribution of

village leader candidate * ’s virtue. The representative village resident or

township official hold identical prior perception on village leader candidate *’s

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virtue, of which the density kernel of her prior distribution is J &' . After

naturally communicating with village leader candidate * for the first time, the

representative village resident or township official updates the density kernel of

the posterior distribution of her virtue as,

(3) K &' Ω'M2 = J &' ∙ O &'; Ω'M2

This posterior distribution in period 3 = 1 is also the previous distribution in

period 3 = 2. After the natural communication in period 3 = 2, the updated

density kernel of posterior distribution is

(4) K &' 0'M2 , 0'D2 = J &' ∙ O &'; 0'M2 ∙ O &'; 0'D

2

= J &' O &'; 0'M2 ∙ O &'; 0'D

2

Repeating this iteration, after ultimately 4 times of natural communication

between the representative village resident or township official and village

leader candidate *, the density kernel of posterior distribution of village leader

candidate *’s virtue (See Appendix A.1) becomes

(5) K &' 0'M2 ∙∙∙ 0'R2 = J &' ∙ [O &'; 0'M2 …O &'; 0'R

2 ]

∝ TUK{− M

D

M

V 2W(&' − X &' )D }

where the posterior mean of village leader candidate *’s virtue is,

(6) X &' =YZC[

YZC[ \RYCH

[ &'7 +

RYCH[

YZC[ \RYCH

[ &'

and the posterior variance of village leader candidate *’s virtue is,

(7) ] &' =YCH[ YZC

[

YZC[ \RYCH

[

Given different ultimate times of natural communication, the representative

village resident in election or the representative township official in

appointment obtains the posterior mean of village leader candidate *’s virtue as,

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(8) X567(899) &' =YZC[

YZC[ \RYCH

[ &'7 +

RYCH[

YZC[ \RYCH

[ &', where 4 = 4567or4899

and obtains the posterior variance of village leader candidate *’s virtue as,

(9) ]567(899) &' =YCH[ YZC

[

YZC[ \RYCH

[ , where 4 = 4567`a4899

Following similar Bayesian inference, the density kernel of posterior

distribution of village leader candidate *’s capacity is (See Appendix A.2)

(10) K )' 0'M< ∙∙∙ 0'R

< = J )' ∙ [O )'; 0'M< …O )'; 0'R

< ]

∝ TUK{− M

D

M

V <W()' − X )' )D }

where the posterior mean of village leader candidate *’s capacity is,

(11) X )' =YbG[

YbG[ \RYGH

[ )'7 +

RYGH[

YbG[ \RYGH

[ )'

and the posterior variance of village leader candidate *’s capacity is,

(12) ] )' =YGH[ Y

bG[

YbG[ \RYGH

[

Therefore, the representative village resident or township official’s posterior

mean of village leader candidate *’s capacity is,

(13) X567(899) )' =YbG[

YbG[ \RYGH

[ )'7 +

RYGH[

YbG[ \RYGH

[ )' where 4 = 4567, 4899

and their posterior variance of village leader candidate *’s capacity is,

(14) ]567(899) )' =YGH[ Y

bG[

YbG[ \RYGH

[ where 4 = 4567, 4899

Proposition 1 discusses how accumulating times of natural communication

improve the inference of village leader candidates’ virtue and capacity.

PROPOSITION 1: As the times of the representative village resident or

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township official’s natural communication with village leader candidates

accumulate, the inference of each village leader candidate’s virtue and capacity

is improve in the following aspects:

(a) The Inference Precision increases with the times of natural communication,

shown by the deceasing posterior variance of virtue (or capacity) with the

ultimate times of natural communication.

(b) The Inference Accuracy increases with the times of natural communication,

shown by the decreasing scaled ratio of the difference between the posterior

mean of virtue (or capacity) and the real value of virtue (or capacity) over the

difference between the prior mean of virtue (or capacity) and the real value of

virtue (or capacity) with the ultimate times of natural communication.

(c) The Marginal Inference Accuracy decreases with the times of natural

communication, shown by the increasing marginal scaled ratio of the difference

between the posterior mean of virtue (or capacity) and the real value of virtue

(or capacity) over the difference between the prior mean of virtue (or capacity)

and the real value of virtue (or capacity) with the ultimate times of natural

communication.

Proof: (a) The first-order derivative of ] &' with respect to 4 is

(15) c[V 2W ]

cR=

dYCHe YZC

[

(YZC[ \RYCH

[ )[< 0

Similarly, the first-order derivative of ] )' with respect to 4 is

(16) c[V <W ]

cR=

dYGHe Y

bG[

(YbG[ \RYGH

[ )[< 0

(b) The scaled ratio of the difference between the posterior mean of virtue

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and the real value of virtue over the difference between the prior mean of virtue

and the real value of virtue is

(17) g 2W d2W2WHd2W

=YZC[

YZC[ \1YCH

[ = V 2WYCH[

Therefore, we have

(18) c[h CW iCWCWHiCW

]

cR= M

YCH[c[V 2W ]

cR< 0

Similarly, the scaled ratio of the difference between the posterior mean of

capacity and the real value of capacity over the difference between the prior

mean of capacity and the real value of capacity is

(19) g <W d<W<WHd<W

=YbG[

YbG[ \RYGH

[ = V <WYGH[

Therefore, we have

(20) c[h GW iGWGWHiGW

]

cR= M

YGH[cV <WcR

< 0

(c) The second-order derivative of ] &' with respect to 4 is

(21) c[V 2WcR[

�DYCH

j YZC[

(YZC[ \RYCH

[ )k> 0

Therefore, the second-order derivative of g 2W d2W2WHd2W

with respect to 4, which

is the marginal scaled ratio of the difference between the posterior mean of

virtue and the real value of virtue over the difference between the prior mean of

virtue and the real value of virtue, is

(22) c[[

h CW iCWCWHiCW

]

cR[= M

YCH[c[V 2WcR[

> 0

Similarly, the second-order derivative of ] )' with respect to 4 is

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(23) c[V <WcR[

�DYGH

j YbG[

(YbG[ \RYGH

[ )k> 0

Therefore, the second-order derivative of g <W d<W<WHd<W

with respect to 4, which

is the marginal scaled ratio of the difference between the posterior mean of

capacity and the real value of capacity over the difference between the prior

mean of capacity and the real value of capacity, is

(24) c[[

h GW iGWGWHiGW

]

cR[= M

YGH[c[V <WcR[

> 0 ∎

Figure 1 shows that as the times of the representative village resident or

township official’s natural communication with village leader candidates

accumulate, (a) the band widths for the squared roots of posterior variances

decease, reflecting the increasing inference precision; (b) the difference

between the posterior mean of virtue (or capacity) and the real value of virtue

(or capacity) decreases, reflecting the increasing inference accuracy; and (c) the

curves of the posterior means are concave in ascending updates and convex in

descending updates, reflecting the decreasing marginal inference accuracy.

The implication of the improved inference precision and accuracy is that each

time of natural communication brings local information on village leader

candidates’ virtue and capacity, and such local information improves the

inference of village leader candidates’ virtue and capacity on precision and

accuracy. For the marginal inference accuracy, the implication is that as the

times of natural communication accumulate, the increment of local information

�Figure 1 is about here��

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for inferring village leader candidates’ virtue and capacity diminishes.

3. Institutional Comparison (Inference Accuracy and Precision): To

compare the inference precision and accuracy after and before introducing local

direct elections, we have an assumption regarding 4567 and 4899 , the

representative village resident’s and the representative township official’s

ultimate times of natural communication with each village leader candidate.

ASSUMPTION 3: 4567 > 4899

Assumption 3 indicates that the representative village resident naturally

communicates with village leader candidates of more times than the

representative township official. The reason is that village leader candidates are

also residents in this representative village, who have long-time and frequent

natural communication with other village residents in various situations (Bell,

2016). For instance, village leader candidates and other village residents usually

know each other since they were very young. As they grow up and live in the

village, they have long-term and frequent communication at school, in

production or commercial activities, and in everyday lives. On the contrary,

village leader candidates have less chances of natural communication with

township officials. The reasons could be that village leader candidates usually

communicate with township officials when dealing with village public affairs

or their private affairs involved with township administration; in addition,

township officials are often posted among different towns.

Given that 4567 > 4899 , we compare the inference precision and the

inference accuracy of each village leader candidate’s virtue and capacity after

and before introducing local direct elections:

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(a) The representative village resident infers village leader candidates’ virtue

and capacity of higher precision before electing one of them as the village leader,

compared to the representative township official does before appointing one of

them as the village leader.

(b) The representative village resident infers village leader candidates’ virtue

and capacity of higher accuracy before electing one of them as the village leader,

compared to the representative township official does before appointing one of

them as the village leader.

As is shown in Figure 1, the band width representing the squared root of the

posterior variance of village leader candidates’ virtue or capacity in election is

smaller than that in appointment, implying the representative village resident’

higher inference precision. The difference between the posterior mean of village

leader candidates’ virtue or capacity and its real value in election is smaller than

that in appointment, implying the implying the representative village resident’

higher inference accuracy.

To sum up, the representative village resident, due to her more times of

natural communication with village leader candidates, have more local

information on village leader candidates’ virtue and capacity than the

representative township official. Therefore, as local direct elections empower

the selection for the village leader to the representative village resident from the

representative township official, village leader candidates’ virtue and capacity

are both inferred of higher precision and accuracy.

B. Selection for Village Leaders

This section discusses how local direct elections, by providing local

information on village leader candidates’ virtue and capacity, facilitate the

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fulfillment of meritocratic selection for village leaders. Specifically, local direct

elections, by providing the inference of higher accuracy on village leader

candidates’ virtue and capacity, improve the mean value of the village leader’s

composite virtue-and-capacity in a representative village. In addition, by

providing the inference of higher precision on village leader candidates’ virtue

and capacity, local direct elections also reduce the variance of the village

leader’s composite virtue-and-capacity in a representative village.

1. Setup: The representative village resident and township official both

would select the village leader candidate with the highest composite virtue-and-

capacity as the village leader. Our theory defines composite virtue-and-capacity

as a weighted average of virtue and capacity, such that n&' + (1 − n))' , of

village leader candidate * , where n represents the weight that the

representative village resident and township official put on village leader

candidates’ virtue, in other words, the preference spectrum over virtue and

capacity, and n ∈ [0, 1].

Mean Value of Composite Virtue-and-Capacity To obtain the composite

virtue-and-capacity of the elected (or appointed) village leader in a

representative village, we calculate the mean value of composite virtue-and-

capacity of all village leader candidates in a representative village that has

already (or has not) introduced the local direct election. To calculate the mean

value of composite virtue-and-capacity of all village leader candidates, we

calculate a weighted average of all village leader candidates’ composite virtue-

and-capacity with weight o', the likelihood that village leader candidate * is

elected or appointed. o' has the following properties:

(a) o' is contingent on village leader candidate * ’s composite virtue-and-

capacity.

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(b) o' ∈ [0, 1], thus its value represents the likelihood of electing or appointing

village leader candidate * as the village leader.

(c) o' is positively associated with village leader candidate *’s virtue and her

capacity, which reflects positive screening of the election and appointment for

village leaders (Dal Bó et al., 2017) upon candidates’ virtue and their capacity.

Specifically, c8Wc2W

> 0 and c8Wc<W

> 0.

To satisfy these three properties, for simplicity and without losing generality,

we use a weighted average of village leader candidate *’s posterior mean of

virtue and her posterior mean of capacity as her likelihood to be elected or

appointed as the village leader, with weight n, the preference spectrum over

virtue and capacity. In the light of Alesina and Tabellini (2007), village leader

candidate *’s likelihood to be elected or appointed that we use here can be

regarded as a reward. This reward is a product of the village leader’s constant

payoff standardized to 1 with village leader candidate * ’s likelihood to be

elected or appointed.

Therefore, the likelihood that village leader candidate * is elected or

appointed takes the form that

(25)� � o' = nX &' + 1 − n X )'

� � � � � � � = n[V 2WYCH[ &'

7 + (1 − V 2WYCH[ )&'] + (1 − n)[

V <WYGH[ )'

7 + (1 − V <WYGH[ ))']�

where ] &' ≡YCH[ YZC

[

YZC[ \RYCH

[ , ] )' ≡YGH[ Y

bG[

YbG[ \RYGH

[ .

As is discussed in Section III.A., ] &' and ] )' measure the inference

precision. As the times of natural communication rise, ] &' and ] )'

decreases and thus o' tends to be the composite virtue-and-capacity. Therefore,

when 4 = 4567 , ] &' = ]567 &' and ] )' = ]567 )' , then we have

o' = o'567, the likelihood that village leader candidate * is elected; when 4 =

� 20

4899 , ] &' = ]899 &' and ] )' = ]899 )' , then we have o' = o'899 ,

the likelihood that village leader candidate * is appointed.

To calculate the weighted average of all village leader candidates’ composite

virtue-and-capacity with weight o' , since o'Mq r&'

Mq r)' < 1, that is, the

sum of weights are smaller than 1, we should have [n&' + (1 −Mq

Mq

n))'] o'r&' r)' , the weighted average of all village leader candidates’

composite virtue-and-capacity, divided by o'Mq r&'

Mq r)' , in order to

standardize the weights. As a result, the mean value of the composite virtue-

and-capacity of the elected (or appointed) village leaders is,

(26 ) n& + 1 − n ) st,567 899 = u567 899 n&' + 1 − n )'

=v2W\ Mdv <W 8W

wxH(yzz){| }2W

{| }<W

8WwxH(yzz){

| }2W{| }<W

�

where the likelihood that village leader candidate * is elected, or appointed, is

(27)� � o'567 899 = nX567 899 &' + 1 − n X567 899 )'

� � � � � � � � � � � � � � = nVwxH yzz 2W

YCH[ &'

7 + 1 −VwxH yzz 2W

YCH[ &' �

� � � � � � � � � � � � � � � � � � +(1 − n)[VwxH(yzz) <W

YGH[ )'

7 + (1 −VwxH(yzz) <W

YGH[ ))']�

where ]567(899) &' ≡YCH[ YZC

[

YZC[ \RwxH(yzz)YCH

[ , ]567(899) )' ≡YGH[ Y

bG[

YbG[ \RwxH(yzz)YGH

[ .

Therefore, it shows that what distinguishes the elected village leader’s and the

appointed village leader’s mean values of the composite virtue-and-capacity in

a representative village is the representative village resident’s and the

representative township official’s different times of natural communication with

village leader candidates.

Variance of Composite Virtue-and-Capacity We could also obtain the

variance of composite virtue-and-capacity of the elected (or appointed) village

� 21

leader in a representative village, by calculating the variance of composite

virtue-and-capacity of all village leader candidates in a representative village

that has already (or has not) introduced the local direct election. By the

definition of variance, the variance of composite virtue-and-capacity of of the

elected (or appointed) village leader in a representative village is,

(28) ~�ast,567(899) n& + 1 − n ) = ~�a567 899 n&' + 1 − n )'

= u567(899) n&' + 1 − n )' D − u567(899)Dn&' + 1 − n )'

This measures to what extent the elected (or appointed) village leader’s

composite virtue-and-capacity varies. Similar to the mean value, it shows that

what distinguishes the elected village leader’s and the appointed village leader’s

variances of the composite virtue-and-capacity in a representative village is also

the representative village resident’s and township official’s different times of

natural communication with village leader candidates.

� � 2. Institutional Comparison (Meritocratic Selection for Village Leaders):

Proposition 2 compares the mean value of the elected village leader’s composite

virtue-and-capacity with that of the appointed village leader.

PROPOSITION 2: The elected village leader’s virtue or capacity exceeds the

appointed village leader’s in a representative village. Specifically, we have

(29) [n& + 1 − n )]st,567 > [n& + 1 − n )]st,899

where [n& + 1 − n )]st,567 = u567 n&' + 1 − n )' , [n& + 1 −

n )]st,899 = u899(n&' + (1 − n))').

Followed are specific cases:

Case 1: When n = 1, that is, the representative village resident or township

official only considers village leader candidates’ virtue.

Case 2: When n = 0, that is, the representative village resident or township

� 22

official only considers village leader candidates’ capacity.

Case 3: When n = M

D, that is, the representative village resident or township

official considers village leader candidates’ virtue and capacity with equal

weights.

Case 4: When n ∈ (MD, 1) , that is, the representative village resident or

township official emphasizes more on virtue. This is contingent on )'7 ∈ [0.5, 1],

that is, the prior mean of each village leader candidate’s capacity is above the

mean of the real values of all potential village leader candidates’ capacity.

Case 5: When n ∈ (0, MD) , that is, the representative village resident or

township emphasizes more on capacity. This is contingent on &'7 ∈ [0.5, 1],

that is, the prior mean of each village leader candidate’s capacity is above the

mean of the real values of all potential village leader candidates’ capacity.

Proof: See Appendix B.1. ∎

The assumption that Case 4 is contingent on is from requirements by OLVC

that village leader candidates satisfy a series of personal characteristics

regarding capacity, such as some diploma or management experience, thus the

mean of the representative village resident’s or township official’s prior

perceptions for village leader candidates’ capacity is larger than or equal to 0.5,

the mean of all village residents’ capacity.

Similarly, the implication assumption that Case 5 is contingent on is from

requirements by OLVC that village leader candidates satisfy a series of personal

characteristics regarding virtue, such as no criminal record or some affiliation

to the CPC, thus the mean of the representative village resident’s or township

official’s prior perceptions for village leader candidates’ virtue is larger than or

� 23

equal to 0.5, the mean of all village residents’ virtue.

Proposition 3 compares the variance of the elected village leader’s composite

virtue-and-capacity with that of the appointed village leader.

PROPOSITION 3: The variance of the elected village leader’s composite

virtue-and-capacity is smaller than the variance of the appointed village

leader’s in a representative village. Specifically, we have

(30) ~�ast,567 n& + 1 − n ) < ~�ast,899 n& + 1 − n )

whatever the value at [0, 1] that n take. It’s denoted that ~�ast,567 n& +

1 − n ) = ~�a567 n&' + 1 − n )' , and that ~�ast,899 n& + 1 −

n ) = ~�a899 n&' + 1 − n )' .

Proof: See Appendix B.2. ∎

In sum, after introducing the local direct election to a representative village,

the village leader’s composite virtue-and-capacity’s mean value increases while

its variance decreases. This implies that by providing local information on

village leader candidates’ virtue and capacity, local direct elections facilitate the

fulfillment of meritocratic selection for village leaders.

�

C. Selection for Village Party Secretaries

This section demonstrates that local direct elections, by providing local

information on village leader candidates’ virtue and capacity, also facilitates the

fulfillment of meritocratic selection for village party secretaries. Specifically,

local direct elections raise the mean value of composite virtue-and-capacity of

village leaders, who are also the main candidates of village party secretaries,

thus elected village leaders are more likely to be promoted, based on their

� 24

performance, as village party secretaries than appointed village leaders. As a

result, the village party secretary’s composite virtue-and-capacity is raised.

1. The Performance-based Promotion for Village Party Secretaries: In a

representative village, village party secretary candidates are usually members

of the village party committee. Similar to the selection for the village leader

discussed above, the representative township official, by naturally

communicating with village party secretary candidates, infers their composite

virtue-and-capacity and appoint the highest one as the village party secretary.

The village leader, also a member of the village party committee, is a special

and the major candidate of village party secretary (O'brien and Li, 2000). Since

the village leader is the major policymaker in the village, her performance in

village economic development is a key signal of her composite virtue-and-

capacity. By observing the village leader’s performance, the representative

township official infers the village leader’s composite virtue-and-capacity and

is likely to promote her as the village party secretary (WRRGOCCP, 1999).

Without losing generality, it is assumed that the village leader’s performance is

a strictly increasing function of her composite virtue-and-capacity, in lights of

Jones and Olken (2005), Besley et al. (2011), Yao and Zhang (2015) and Bloom

et al. (2015). Specifically,

(31) Ç = ℱ[(n& + 1 − n ))st] + Ñ

where Ç represents the village leader’s performance, (n& + 1 − n ))st

represents her composite virtue-and-capacity, and Ñ represents the random

error, where Ñ~?(0, AÖD). ℱ[∙] is strictly increasing in (n& + 1 − n ))st.

The likelihood to appoint the village leader as the village party secretary is

specified as

(32) Ü = á (n& + 1 − n ))st|Ç

� 25

which is, similar to Section III.B., the posterior mean of composite virtue-and-

capacity of the village leader by observing her performance.

To specify (32), the posterior mean of composite virtue-and-capacity, similar

to Section III.A., we first assume the representative township official’s prior

perception on the village leader’s, either elected or appointed, composite virtue-

and-capacity distributed as

ASSUMPTION 4 (Prior distribution on the village leader’s virtue and capacity):

The representative township official’s prior perception on the village leader’s

virtue is distributed as ? &â, A2äD , truncated at 0,1 , where &â ∈ [0, 1]. Her

prior perception on the village leader’s capacity is distributed as ? )â, A<äD ,

truncated at 0,1 , where )â ∈ [0, 1]. &â and )â, the prior means, and A2äD

and A<äD , the prior variances, are known to the representative township official.

The prior distribution of village party secretary candidate ã ’s composite

virtue-and-capacity is thus a normal distribution ? nD&â + (1 − n)D)â, A2äD +

A<äD , truncated at 0,1 , according to the convolution formula. Using the

similar Bayesian framework as in Section III.A., the posterior mean of the

composite virtue-and-capacity of the village leader is (See Appendix C),

(33) á (n& + 1 − n ))st|Ç

= 1 − å nD&â + (1 − n)D)â + åℱ (n& + 1 − n ))st

where n ∈ (0,1), å ≡YCä[ \YGä

[

YCä[ \YGä

[ \Yç[.

2. Institutional Comparison (Meritocratic Selection for Village Party

Secretaries): In this part we first compare the elected village leader’s and the

� 26

appointed village leader’s likelihood to be promoted as the village party

secretary, in a representative village. Then we compare the village party

secretary’s composite virtue-and-capacity before and after introducing the local

direct election.

Before comparing the likelihood to be promoted as the village party secretary

in a performance-based promotion, we need another assumption:

ASSUMPTION 5: The introduction of local direct elections only influences

village leaders’ composite virtue-and-capacity, not other village party secretary

candidates’ composite virtue-and-capacity.

With Assumption 5, we have the following proposition:

PROPOSITION 4: (The Elected Village Leader’s Higher Promotion

Likelihood): In a representative village with the performance-based promotion

for the village party secretary, the elected village leader, due to her higher

composite virtue-and-capacity, has higher likelihood to be promoted as the

village party secretary, compared to the appointed village leader.

Proof: Section III.B. has shown that in a representative village, the elected

village leader’s composite virtue-and-capacity exceeds the appointed village

leader’s, that is, [n& + 1 − n )]st,567 > [n& + 1 − n )]st,899.

Based on (31), we know that

(34) ℱ [n& + 1 − n )]st,567 > ℱ [n& + 1 − n )]st,899

Following (33), the likelihood of the elected (or appointed) village leader to

be promoted as the village party secretary is specified as

� 27

(35) Ü567(899) = á (n& + 1 − n ))st|Ç567(899)

= 1 − å nD&â + (1 − n)D)â + åℱ[[n& + 1 − n )]st,567(899)]

where n ∈ (0,1), å ≡YCä[ \YGä

[

YCä[ \YGä

[ \Yç[.

According to (34), we know that Ü567 > Ü899. ∎

Proposition 4 shows that because what underlies the village leader’s

promotion likelihood is her composite virtue-and-capacity revealed through her

performance, and the elected village leader’s mean value of composite virtue-

and-capacity exceeds the appointed one’s, thus the elected village leader’s

promotion likelihood surpasses the appointed one’s.

� � By comparing, in a representative village, the elected and appointed village

leader’s promotion likelihood, we have

(36) Ü567 899 = åΓè + åℱ [[n& + 1 − n )]st,899

+ 1 − å nD&â + (1 − n)D)â

where Γ ≡ ℱ [[n& + 1 − n )]st,567 − ℱ[[n& + 1 − n )]st,899 , è ≡

è{= 1, *êTëTí3Tr;= 0, *ê�KK`*ì3Tr} is the indicator, å ≡YCä[ \YGä

[

YCä[ \YGä

[ \Yç[.

åℱ [[n& + 1 − n )]st,899 is named as the performance-based promotion

premium, implying the appointed village leader’s promotion likelihood as the

village party secretary explained by her performance observed. This shows that

the performance-based promotion scheme is an ex post assessment for the

village leader, because it incentivizes politicians and holds them accountable,

as is discussed in previous studies (Dewatripont et al., 1999; Alesina and

Tabellini, 2007).

åΓè is named as the local information increment, implying the elected

village leader’s promotion likelihood increment, compared to the appointed

� 28

village leader, as the village party secretary, which is explained by the elected

village leader’s performance observed. This shows that integrated with local

direct elections, the performance-based promotion scheme is also an ex ante

meritocratic selection for the village leader. Local direct elections provide local

information on village leader candidates’ virtue and capacity and upon which

raise the composite virtue-and-capacity of the village leader. Therefore, in a

performance-based promotion scheme, the elected village leader with her

higher composite virtue-and-capacity, has an increment of the likelihood to be

promoted as the village party secretary, compared to the appointed one.

We further provide a Corollary of Proposition 4 showing how local direct

elections facilitate the fulfillment of meritocratic selection for the village party

secretary. Suppose there are two village party secretary candidates: the village

leader and a representative other candidate. The elected (or appointed) village

leader’s composite virtue-and-capacity is [n& + 1 − n )]st,567(899) and her

promotion likelihood is Ü567 899 . The representative other candidate’s

composite virtue-and-capacity is [n& + 1 − n )]î1ï7ñ and her promotion

likelihood is assumed to be 1 − Ü567 899 . According to Assumption 5,

[n& + 1 − n )]î1ï7ñ is uncorrelated with whether introducing the local direct

election or not. Therefore, we have,

COROLLARY (Meritocratic Selection for Village Party Secretaries): After

introducing the local direct election to a representative village, the village party

secretary’s composite virtue-and-capacity is raised. Specifically, we have

(37) [n& + 1 − n )]sóg,567 > [n& + 1 − n )]sóg,899

Proof: we know that

� 29

(38) n& + 1 − n ) sóg,567

= n& + 1 − n ) st,567Ü567 + n& + 1 − n ) î1ï7ñ 1 − Ü567

= Ü567 n& + 1 − n ) st,567 − n& + 1 − n ) î1ï7ñ

+ n& + 1 − n ) î1ï7ñ

and that

(39) n& + 1 − n ) sóg,899

= n& + 1 − n ) st,899Ü899 + n& + 1 − n ) î1ï7ñ 1 − Ü899

= Ü899 n& + 1 − n ) st,899 − n& + 1 − n ) î1ï7ñ

+ n& + 1 − n ) î1ï7ñ

Since Proposition 2 implies that [n& + 1 − n )]st,567 > [n& + 1 −

n )]st,899 and Proposition 4 implies that Ü567 > Ü899, we know that

(40) n& + 1 − n ) sóg,567 > n& + 1 − n ) sóg,899 ∎

D. Summary

This section demonstrates that local direct elections, by providing local

information on village leader candidates’ virtue and capacity, facilitate the

fulfillment of meritocratic selection both for village leaders and for village party

secretaries, yet in different ways.

Local direct elections facilitate the fulfillment of meritocratic selection for

village leaders directly, by providing the local information on village leader

candidates and through which improving the screening effects. Specifically,

after local direct elections empower the selection for village leaders, who have

more times of natural communication with village leader candidates than

township officials, village leader candidates’ virtue and capacity are posteriorly

inferred of better screening effects, that is, of higher precision and accuracy. As

a result, the mean values of village leaders’ composite virtue-and-capacity rises

� 30

while the variances of that drops. With the preference spectrum over virtue and

capacity, our theory apply for a continuum of scenarios of selection for leader

from the purely virtue-oriented to the purely capacity-oriented.

On the contrary, local direct elections facilitate the fulfillment of meritocratic

selection for village party secretaries indirectly, by providing the local

information on village leader candidates and through which improving the

candidate pool. Specifically, since village leaders are the main candidates for

village party secretaries, and the mean values of village leaders’ composite

virtue-and-capacity rises,

IV. Empirical Evidence

In this section, we first introduce the sampling method and data. Then we

introduce the empirical evidence supporting the meritocratic selection for

village leaders in rural China. Finally, we introduce the empirical evidence

supporting the meritocratic selection for village party secretaries in rural China.

A. Sampling and Data

The sampling and data used in this paper are the same as used in Wong et al.

(2017). The 101 sampled villages representing five major agro-ecological zones

in China were surveyed three times (in 2005, 2008 and 2012). We obtain

detailed information in these 101 villages on village public goods, local

governance and local socio-economic conditions, which ranges from 1995 to

2012 and contains five office terms (approximately three years per term).

In these 101 villages, we obtain reliable and comprehensive project quality

measures of 563 village roads in total. To ensure the measure precision, the field

team worked with professional civil engineers and the transportation

departments of local governments, before field surveys, to develop a standard

� 31

and scientific village road quality evaluating scheme. A series of measures was

also taken to avoid enumerator-specific subjectiveness on village road projects8.

By adding up all partial quality scores, the comprehensive village road quality

score (0-100 points) for these 563 village roads is obtained.

We consider project quality of village roads influenced both by village leaders’

virtue and by their capacity; therefore, it reflects village leaders’ composite

virtue-and-capacity. The reason is that it is village leaders’ capacity that

influences the investment of village public road projects (Martinez-Bravo et al.,

2011); yet making good use of the investment and transforming it to the quality

require village leaders’ virtue, including, but not limited to, responsibility and

intrinsic motives to serve local people (Tian et al., 2013).

B. Evidence of the Meritocratic Selection for Village Leaders

The data used in this section is the “road-construction year” panel data set

used in Wong et al. (2017). Our data use the mean value of village road quality

to represent the mean value of village leaders’ composite virtue-and-capacity,

and uses the variance of village road quality to represent the variance of village

leaders’ composite virtue-and-capacity. The mean value of village road quality

by elected village leaders is 80.27, while that by appointed village leaders is

60.18. On the contrary, the variance of village road quality by elected village

leaders is 123.29 while that by appointed village leaders is 195.07. Figure 2

shows histograms of village road quality by either elected or appointed village

leader, and illustrates similar results as above. In a word, local direct elections

���������������������������������������� ����8 For details on avoiding measurement errors in project quality of village roads, see Wong et al. (2017).

�Figure 2 is about here��

� 32

facilitate the fulfillment of meritocratic selection for village leaders.

Wong et al. (2017) also provides econometric estimation results as evidence

for elected village leaders’ higher mean value of composite virtue-and-capacity

than appointed village leaders’. The econometric specification is

(41) òë3ôöñõ = úq + úMáëTöõ + +ùöñõû + üö + †õ + °ö1

where òë3ôö¢ is the quality of village road a built starting in year of £ in

village §. áëTöõ is a dummy variable whether the village leader who built the

road starting in year of £ in village § was elected directly by local village

residents. ùöñõ represents controlling variables, üö is the village dummy and

†õ is the road project starting year dummy. °ö1 is the random error,

The estimation results in Wong et al. (2017), show that after introducing local

direct elections, the village road quality is increased on average. Since village

leaders’ composite virtue-and-capacity underlies the village road quality, these

estimation results imply elected village leaders’ higher mean value of composite

virtue-and-capacity than appointed village leaders’.

C. Evidence of the Meritocratic Selection for Village Party Secretaries

The meritocratic selection for village party secretaries can be empirically

testified, according to Section III.C., by comparing, in a representative village,

the association between elected village leaders’ performance with their

likelihood to be promoted as village party secretaries, and that association of

appointed village leaders. Based on (36), the specification is

(42) Üö1 = úq + úMáëTö1 + úDoòë3ôö1 + ú•áëTö1 ∙ oòë3ôö1

+¶ö1ß + üö + ®1 + ©ö1

where Üö1 is a dummy variable whether the village leader is promoted as the

� 33

village party secretary as her tenure ends. In village §, if the village leader

would be promoted as the village party secretary as her village leader tenure

ends in year 3, the value of Üö1 of this observation is 1; otherwise it is 0. áëTö1

is a dummy variable whether this village leader was elected directly by local

village residents. oòë3ôö1 is the average project quality of village roads in this

village leader’s tenure.

¶ö1 represents the controlling variables, that is, the characteristics of village

§, of the village leader, and of the party secretary incumbent in the village

leader’s tenure-ending year 3. We control for population and per capita income

in the village, village leaders’ age and years of schooling, and party secretary

incumbents’ age. In addition, üö and ®1 represents the village fixed effects

and the tenure-ending year fixed effects, respectively. ©ö1 is the random error.

Different from the “road-construction year” panel data set used in Section

III.B., this section uses the “village-tenure” panel data set. Since partial village

leaders hold the position for more than one term, in each village, we regard the

village leader’s whole tenure (one or more terms) as one observation. Therefore,

a village-tenure panel data set is obtained, where the tenure is marked with the

village leader’s tenure-ending year. On average, there are 4-5 village leaders in

each of the 101 villages from 1995 to 2012. Therefore, our village-tenure panel

data set contains 455 observations, in which the average project quality of

village roads in each village leader’s tenure is also calculated.

Online Appendix Table 1 presents the summary statistics of variables used in

our study. Table 1 presents the estimation results of our specifications. Column

�Table 1 is about here��

� 34

1 shows that úM is significantly positive. This result is consistent with our

Proposition 4 that the elected village leader in a representative village receives

higher promotion likelihood.

The result in Column 2 of Table 1 shows that úD is significantly positive, in

other words, the average project quality of village roads observed by township

officials has statistical evidence to contribute to appointed village leaders’

average promotion likelihood. This result is consistent with our theoretical

prediction of the performance-based promotion premium, in other words,

úDoòë3ôö1 matches åℱ [[n& + 1 − n )]st,899 in (36).

The result in Column 2 of Table 1 also shows that ú• is significantly positive,

that is, the average project quality of village roads contributes, statistically, to

elected village leaders’ average promotion likelihood to a larger extent than to

appointed village leaders’. This result is consistent with our theoretical

prediction of local information increment, in other words, ú•áëTö1 ∙ oòë3ôö1

matches åΓè in (36).

V. Concluding Remarks

Two major issues in political economy, both concerns information asymmetry,

are political selection that may suffer from adverse selection and political

incentive that could suffer from moral hazards. In addressing moral hazards,

accumulating studies have been conducted, either by deciphering existing

schemes or by designing new mechanisms, to discuss the fulfillment of

accountability of politicians (Laffont, 2000; Besley, 2006). Addressing adverse

selection, however, appears commonly in literature regarding, for instance, job

market signaling (Spence, 1973) and product advertisement (Milgrom and

Roberts, 1986), yet seldom in political selection literature. Both types of issues,

� 35

in existing studies, are basically discussed under the game theory framework.

In lights of local information (Hayek, 1945), we discover new ways to

address adverse selection in political selection with the Bayesian framework.

We demonstrate that local direct elections facilitate the fulfillment of

meritocratic selection for village leaders directly, by providing the local

information on village leader candidates and through which improving the

screening effects. This demonstration is empirically supported9.

We further demonstrate theoretically and empirically that integrating local

information with ex post incentives facilitates addressing adverse selection and

moral hazards in political selection, endowing the performance-based

promotion with meritocratic selection. Specifically, local direct elections

facilitate the fulfillment of meritocratic selection for village party secretaries

indirectly, by providing the local information on village leader candidates and

through which improving the candidate pool.

Several limitations and extensions are important to note. First, although

assumption in our model that political selections in rural China law-abiding

could partially deviate from facts, our theoretical predictions on meritocratic

selection for village leaders and for village party secretaries are supported

empirically. Second, it’s a strong assumption that the election or appointment

likelihood for village leaders equal to village leader a weighted average of

village leader candidates’ posterior virtue and posterior capacity, and some

further discussion is in need to relax this assumption. Third, although it is

interesting to discuss whether the meritocratic selection for village leaders

���������������������������������������� ����9 Given the previously discussed assumption that politicians’ performance is an increasing function of

their composite virtue-and-capacity, our demonstration is empirically supported by studies regarding the

impacts of local direct elections on village public investment (Luo et al., 2007; Martinez-Bravo et al.,

2014), and studies regarding that on quality of village public infrastructure (Wong et al. 2017).

� 36

facilitates by local direct elections leads to an equilibrium in which village

leaders, village residents and township officials all obtain optimized payoffs,

due to limited spaces, it is not discussed in this paper.

� 37

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� 41

FIGURE 1: INFERENCE ACCURARY AND PRECISION WITH NATURAL COMMUNICATION TIMES

� 42

�

���

FIGURE 2: HISTOGRAM OF ROAD QUALITY BY ELECTION OR APPOINTMENT

05

10

40 60 80 100 40 60 80 100Source: Authors' survey Source: Authors' survey

Roads built by appointed leaders Roads built by elected leaders

Perc

ent o

f villa

ge ro

ad p

roje

cts

Road quality scoresGraphs by institution

� 43

Online Appendix Table 1: Summary statistics of sample village road projects and sample villages

N Mean S.D. Min Max

Explained variables

Village leader promoted as party secretary as her tenure ends (Y=1; N=0) 455 0.248 0.433 0 1

Main explanatory variable

Village leader elected (Y=1; N=0) 455 0.547 0.498 0 1

Average comprehensive road quality scores of all village road projects in the village leader’s tenure 226 71.353 16.123 26.75 98.9

Village leader characteristics

Age 455 50.147 4.775 36 63

Years of Schooling 455 9.435 2.459 5 16

Party secretary incumbent characteristics

Age 455 53.668 5.642 41 68

Village characteristics

Village population (in 1,000 persons) 455 1.912 1.387 0.16 6.60

Village per capita income (in 1,000 yuan) 455 3.455 1.887 0.30 10.15

Data source: Authors’ survey

� 44

Table 1: FE estimates of the impacts of village election and village road project quality on village leaders’ promotion likelihood as village party secretaries

Explained variable: Village leader promoted as village party secretary (Y=1; N=0)

(1) (2)

Village leader elected

(Y=1; N=0)

0.160***

(0.061)

-0.034

(0.058)

Average comprehensive road quality scores of all village road projects in

the village leader’s tenure (0-100)

0.0019**

(0.0010)

Village leader elected × Average comprehensive road quality scores of

all village road projects in the village leader’s tenure (0-100)

0.0030**

(0.0012)

Village characteristics Y Y

Village leader characteristics Y Y

Party secretary incumbent characteristics Y Y

Village FE & Tenure-ending year FE Y Y

N 455 455

R2 0.06 0.16

Data source: Authors’ survey

Note: All models control for characteristics of villages, village leaders and party secretary incumbents, and village fixed effects and tenure-ending year fixed effects. Village characteristics include village population and village per

capita income. Village leaders’ characteristics include age and years of schooling. Party secretary incumbents’ characteristics include age. Linear probability models are used in this table. Robust standard errors, clustered at the

village level, are reported in parentheses. ***, **, and * indicate statistical significance from zero at the 1, 5, and 10 percent levels.

� 45

Online Appendix for Local Direct Elections, Local Information and Meritocratic

Selection

A. Posterior Distributions of Virtue and Capacity

A.1 Virtue: In the light of Koop et al. (2007), we derive the density kernel of the

posterior distribution of virtue, such that

(A1) ! "# $%&' = ) "# ∙ [, "#; .#/0 …, "#; .#2

0 … , "#; .#30 ]]

where the vector $%&' is [.#/0 ….#20 ….#30 ].

First, we derive ) "# , the density kernel of the prior distribution of virtue. Since

the prior distribution is a normal distribution truncated at [0, 1], we have

(A2) ) "# = ) "# 0 ≤ "# ≤ 1, "#9)

=<

=>?@ A[

>BC>B?

=>?@ ]

D 0B EF0BF/,0B?)

=GHI>?

@ C<@∙9JK

C >BC>B? @

@=>?@

D 0B EF0BF/,0B?)

∝9JK{

C >BC>B? @

@=>?@ }

D 0B EF0BF/,0B?)

where O "# 0 ≤ "# ≤ 1, "#9) = P(

/R0B?

I>?@ ) − P(

R0B?

I>?@ ) represents the likelihood that "#

is at [0, 1], contingent on "#9.

Second, we derive the joint density of $%&' as a likelihood function that

(A3) , "#; $%&' = 2UVW>G R

<@ ∙ XY!

R ZB[>R0B

@

GI\>@

32]/

= 2UVW>G R

^@ ∙ XY! −

ZB[>R0B

@

GI\>@

32]/

∝ XY! −ZB[>R0B

@

GI\>@

32]/

∝ XY! −ZB[>RZ_

>`Z_>R0B

@

GI\>@

32]/

∝ XY! −/

GI\>@ [ .#2

0 − .a0 G32]/ + .a0 − "# G3

2]/ + 2 .#20 − .a0 .a0 − "#3

2]/

where .a0 =/

3.#203

2]/ . Because .#20 − Ωa0 G3

2]/ , the second-order moment, is a

� 46

constant, 2 .#20 − Ωa0 .a0 − "#3

2]/ = 2 .a0 − "# .#20 − Ωa03

2]/ = 0, we have

(A4) , "#; $%&' ∝ XY! −Z_>R0B

@

GI\>@

32]/ ∝ XY! −d

Z_>R0B

@

GI\>@

Thirdly, by Bayes’ rule, the density kernel of posterior distribution of virtue is

(A5) , "#; $%&' ) "# ∝

9JK R3e_>C>B

@

@=\>@ fgh

C >BC>B? @

@=>?@

D 0B EF0BF/,0B?)

∝9JK R

^

=\>@

e_>C>B

@

@9JK R

<

=>?@

>BC>B? @

@

D 0B EF0BF/,0B?)

∝R<@9JK

^

=\>@ Z_

>R0B@`

<

=>?@ 0BR0B

? @

D 0B EF0BF/,0B?)

∝^

=\>@ Z_

>@RG0BZ_>`0B

@ `<

=>?@ 0B

@RG0B?0B`0B

?@

D 0B EF0BF/,0B?)

∝^

=\>@ `

<

=>?@ 0B

@RG<

=>?@ 0B

?`^

=\>@ Z_

> 0B`^

=\>@ Z_

>@`<

=>?@ 0B

?@

D 0B EF0BF/,0B?)

∝

<

=\>@ =>?

@

=\>@ i^=>?

@

0B@RG

=\>@ =

>?@

=\>@ i^=>?

@<

=>?@ >B

?i^

=\>@ e_

>

=\>@ =>?

@

=\>@ i^=>?

@

0B`^

=\>@ Z_

>@`<

=>?@ 0B

?@

D 0B EF0BF/,0B?)

(A5) is positively associated with

<

=\>@ =>?

@

=\>@ i^=>?

@

0B@RG

=\>@ =

>?@

=\>@ i^=>?

@<

=>?@ >B

?i^

=\>@ e_

>

=\>@ =>?

@

=\>@ i^=>?

@

0B

D 0B EF0BF/,0B?)

after

dropping the constants uncorrelated with "#. Then we have

(A6) , "#; $%&' ) "# ∝

9JK R<@[

<

=\>@ =>?

@

=\>@ i^=>?

@

[0BR{=\>@ =

>?@

=\>@ i^=>?

@<

=>?@ 0B

?`^

=\>@ Z_

> }]@]

D 0B EF0BF/,0B?)

where O "# 0 ≤ "# ≤ 1, "#9) = P(

/R0B?

I>?@ ) − P(

R0B?

I>?@ ). Therefore, this density kernel is

still of a truncated normal distribution, in which the posterior variance of virtue is

(A7) j "# =I\>@ I>?

@

I\>@ `3I>?

@

and the posterior mean of virtue is

(A8) k "# = j "#/

I>?@ "#

9 +3

I\>@ .a0 =

I\>@

I\>@ `3I>?

@ "#9 +

3I>?@

I\>@ `3I>?

@ .a0

� 47

Since .#20~m("#, VW>G ), and d = dno9 dpKK → +∞, we have

(A9) .a0 =/

3.#203

2]/ = s .#20 = "#

thus the posterior mean of virtue is

(A10) k "# =I\>@

I\>@ `3I>?

@ "#9 +

3I>?@

I\>@ `3I>?

@ "#

A.2 Capacity: Similar to virtue, we derive the density kernel of the posterior

distribution of virtue, such that

(A11) ! t# $%&u = ) t# ∙ [, t#; .#/

v …, t#; .#2v … , t#; .#3

v ]]

where the vector $%&u is [.#/v ….#2v ….#3v ].

First, we derive ) t# , the density kernel of the prior distribution of capacity. Since

the prior distribution is a normal distribution truncated at [0, 1], we have

(A12) ) t# = ) t# 0 ≤ t# ≤ 1, t#9)

∝9JK{

C wBCwB? @

@=w?@ }

D vB EFvBF/,vB?)

where O t# 0 ≤ t# ≤ 1, t#9) = P(

/RvB?

Iw?@ ) − P(

RvB?

Iw?@ ) represents the likelihood that t#

is at [0, 1], contingent on t#9.

Second, we derive the joint density of $%&u as a likelihood function that

(A13) , t#; $%&u = 2UVxw

G R<@ ∙ XY!

R ZB[wRvB

@

GIyw@

32]/

∝ XY! −ZB[wRZ_

w`Z_wRvB

@

GIyw@

32]/

∝ XY! R/

GIyw@ [ .#2

v − .avG3

2]/ + .av − t#G3

2]/ + 2 .#2v − .av .av − t#3

2]/

where .av =/

3.#2v3

2]/ . Because .#2v − .av

G32]/ , the second-order moment, is a

constant, 2 .#2v − .av .av − t#3

2]/ = 2 .av − t# .#2v − .av3

2]/ = 0, we have

(A14) , t#; $%&u ∝ XY! −

Z_wRvB

@

GIyw@

32]/ ∝ XY! −d

Z_wRvB

@

GIyw@

� 48

Thirdly, by Bayes’ rule, the density kernel of posterior distribution of capacity is

(A15) , t#; $%&u ) t# ∝

9JK R3e_wCwB

@

@=yw@ fgh

C wBCwB? @

@=>?@

D vB EFvBF/,vB?)

∝9JK R

^

=yw@

e_wCwB

@

@9JK R

<

=w?@

wBCwB? @

@

D vB EFvBF/,vB?)

∝R<@9JK

^

=yw@ Z_

wRvB@`

<

=w?@ vBRvB

? @

D vB EFvBF/,vB?)

∝

^

=yw@ Z_

w@RGvBZ_

w`vB@ `

<

=w?@ vB

@RGvB?vB`vB

?@

D vB EFvBF/,vB?)

∝

^

=yw@ `

<

=w?@ vB

@RG<

=w?@ vB

?`^

=yw@ Z_

w vB`^

=yw@ Z_

w@`

<

=w?@ vB

?@

D vB EFvBF/,vB?)

∝

<

=yw@ =w?

@

=yw@ i^=w?

@

vB@RG

=yw@ =

w?@

=yw@ i^=w?

@<

=w?@ wB

?i^

=yw@ e_

w

=yw@ =w?

@

=yw@ i^=w?

@

vB`^

=yw@ Z_

w@`

<

=w?@ vB

?@

D vB EFvBF/,vB?)

(A15) is positively associated with /=yw@ =w?

@

=yw@ i^=w?

@

t#G − 2

=yw@ =

w?@

=yw@ i^=w?

@<

=w?@ vB

?`^

=yw@ Z_

w

=yw@ =w?

@

=yw@ i^=w?

@

t# after

dropping the constants uncorrelated with t#. Then we have

(A16) , t#; $%&u ) t# ∝

9JK R<@[

<

=yw@ =w?

@

=yw@ i^=w?

@

[vBR{=yw@ =

w?@

=yw@ i^=w?

@<

=w?@ vB

?`^

=yw@ Z_

w }]@]

D vB EFvBF/,vB?)

where O t# 0 ≤ t# ≤ 1, t#9) = P(

/RvB?

Iw?@ ) − P(

RvB?

Iw?@ ). Therefore, this density kernel is

still of a truncated normal distribution, in which the posterior variance of capacity is

(A17) j t# =Iyw@ Iw?

@

Iyw@ `3Iw?

@

and the posterior mean of capacity is

(A18) k t# = j t#/

Iw?@ t#

9 +3

Iyw@ .av =

Iyw@

Iyw@ `3Iw?

@ t#9 +

3Iw?@

Iyw@ `3Iw?

@ .av

Since .#2v~m(t#, VxwG ), and d = dno9 dpKK → +∞, we have

� 49

(A19) .av =/

3.#2v3

2]/ = s .#2v = t#

thus the posterior mean of capacity is

(A20) k t# =Iyw@

Iyw@ `3Iw?

@ t#9 +

3Iw?@

Iyw@ `3Iw?

@ t#

B. Comparing Elected and Appointed Village Leaders’ Mean Values and

Variances of Composite Virtue-and-Capacity

B.1 Mean Values: We compare, in a representative village, the elected and the

appointed village leader’s mean values of composite virtue-and-capacity. Specifically,

we compare

(B1) {no9(|"# + (1 − |)t#) =}0B` /R} vB pB

~�?<Ä Å0B

<Ä ÅvB

pB~�?<

Ä Å0B<Ä ÅvB

and

(B2) {pKK(|"# + (1 − |)t#) =}0B` /R} vB pB

ÇÉÉ<Ä Å0B

<Ä ÅvB

pBÇÉÉ<

Ä Å0B<Ä ÅvB

and we know that

(B3) Ñ#no9 pKK = |kno9 pKK "# + 1 − | kno9 pKK t#

where

(B4) kno9 pKK "# =Ö~�? ÇÉÉ 0B

I>?@ "#

9 + 1 −Ö~�? ÇÉÉ 0B

I>?@ "#

=I\>@

I\>@ `3~�?(ÇÉÉ)I>?

@ "#9 +

3~�?(ÇÉÉ)I>?@

I\>@ `3~�?(ÇÉÉ)I>?

@ "#

(B5) kno9 pKK t# =Ö~�? ÇÉÉ vB

Iw?@ t#

9 + 1 −Ö~�? ÇÉÉ vB

Iw?@ t#

=Iyw@

Iyw@ `3~�?(ÇÉÉ)Iw?

@ t#9 +

3~�?(ÇÉÉ)Iw?@

Iyw@ `3~�?(ÇÉÉ)Iw?

@ t#

Since dno9 > dpKK, comparing the elected and appointed village leader’s composite

virtue-and-capacity is equivalent to having

(B6) á Y à , â à =}0B` /R} vB }ä 0B ` /R} ä vB Å0B ÅvB

<Ä

<Ä

}ä~�? 0B ` /R} ä~�? vB Å0B ÅvB<Ä

<Ä

where k "# = 1 − Y "#9 + Y"# , Y ≡

I>?@ 2

Iå>@ `I>?

@ 2; k t# = 1 − â t#

9 + ât# , â ≡

Iw?@ 2

Iyw@ `Iw?

@ 2. à = dno9çédpKK. Then we need to prove that

� 50

(B7) èêè2=

èê

èJ∙èJ

è2+

èê

èë∙èë

è2> 0

It is easy to prove that èJè2> 0, and èë

è2> 0, so we only need to prove that èê

èJ≥ 0

and èêèë≥ 0.

Firstly, simplify the numerator of (B6) as

|"# + 1 − | t# | 1 − Y "#9 + Y"# + 1 − | 1 − â t#

9 + ât# ì"# ìt#/

E

/

E

=|G"# 1 − Y "#

9 + Y"# + 1 − | Gt# 1 − â t#9 + ât#

+| 1 − | "# 1 − â t#9 + ât# + | 1 − | t# 1 − Y "#

9 + Y"#ì"# ìt#

/

E

/

E

where

(B8) |G"# 1 − Y "#9 + Y"# = |G 1 − Y "#

9"#ì"# ìt#/E

/E

+ |GY"#Gì"# ìt#

/E

/E

= /

G|G 1 − Y "#

9 +/

î|GY

(B9) 1 − | 1 − â t#9 + ât#

= 1 − | G 1 − â t#9t#ì"# ìt#

/E

/E

+ 1 − | Gât#Gì"# ìt#

/E

/E

= /

G1 − | G 1 − â t#

9 +/

î1 − | Gâ

(B10) | 1 − | "# 1 − â t#9 + ât#

= | 1 − | "# 1 − â t#9ì"# ìt#

/E

/E

+ | 1 − | "#ât#ì"# ìt#/E

/E

= /

G| 1 − | 1 − â t#

9 +/

ï| 1 − | â

(B11) | 1 − | t# 1 − Y "#9 + Y"#

= | 1 − | 1 − Y "#9t#ì"# ìt#

/E

/E

+ | 1 − | Y"#t#ì"# ìt#/E

/E

= /

G| 1 − | 1 − Y "#

9 +/

ï| 1 − | Y

Therefore, (B6)’s numerator becomes:

(B12) /G| 1 − Y "#

9 +/

G1 − | 1 − â t#

9 +/

/G| | + 3 Y +

/

/G| − 4 | − 1 â

Secondly, simplify the denominator of (B6)

(B13) | 1 − Y "#9 + Y"# + 1 − | 1 − â t#

9 + ât# ì"# ìt#/E

/E

= | 1 − Y "#9 ì"# ìt#

/E

/E

+ |Y"# ì"# ìt#/E

/E

� 51

+ 1 − | 1 − â t#9 ì"# ìt#

/E

/E

+ 1 − | ât# ì"# ìt#/E

/E

= | 1 − Y "#9 +

/

G|Y + 1 − | 1 − â t#

9 +/

G1 − | â

Accordingly, (B6) becomes

(B14) á Y à , â à =<@} /RJ 0B

?`<@/R} /Rë vB

?`<<@} }`î J`

<<@

}Rï }R/ ë

} /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë

where (B14)’s numerator’s first-order derivative with respect to Y is −/

G|"#

9 +

/

/G| | + 3 , (B14)’s denominator’s first-order derivative with respect to Y is

−|"#9 +

/

G|.

Then we could derive that

(B15) èêèJ=

<<@}ò0B

?`<<@} /R} @ë0B

?`<<@}@ /R} /Rë vB

?`<@ô} /R} G}R/ ë

} /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë

@

=<<@}ò0B

?`<<@}@ /R} /Rë vB

?`<@ô} /R} ë G} /R0B

? `G0B?R/

} /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë

@

To ensure èêèJ≥ 0, we need to have, as is shown in the first step of (B15), 2| − 1 ≥

0, that is, 1 ≥ | ≥/

G, or | = 0. However, when 0 < | <

/

G, we need to reorganize the

numerator items in (B15), as is shown in the second step of (B15), that when we have

2| 1 − "#9 + 2"#

9 − 1 ≥ 2| 1 − "#9 ≥ 0, that is, "#9 ≥

/

G, then we have èê

èJ≥ 0. In

a word, èêèJ≥ 0 when 1 ≥ | ≥

/

G, or | = 0, or both 0 < | <

/

G and "#9 ≥

/

G.

Now we discuss èêèë

. (B14)’s numerator’s first-order derivative with respect to â is

= −/

G1 − | ∙ t#

9 +/

/G| − 4 | − 1 , (B14)’s denominator’s first-order derivative

with respect to â is − 1 − | ∙ t#9 +

/

G1 − | .

Then we could derive that

(B16) èêèë=

<<@}@ /R} JvB

?`<<@

/R} òvB?`

<<@} /R} @ /RJ 0B

?`<@ô} /R} J /RG}

} /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë

@

� 52

=<<@

/R} òvB?`

<<@} /R} @ /RJ 0B

?`<@ô} /R} J /RG}`G}∙vB

?

} /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë

@

To ensure èêèë≥ 0, we need to have, as is shown in the first step of (B16), 1 − 2| ≥

0, that is, 0 ≤ | ≤/

G, or | = 1. However, when /

G< | < 1, we need to reorganize the

numerator items in (B16), as is shown in the second step of (B16), that when we have

1 − 2| + 2| ∙ t#9 ≥ 1 − 2| + õ ≥ 0, that is, t#9 ≥

/

G, then we have èê

èë≥ 0. In a word,

èê

èë≥ 0 when 0 ≤ | ≤

/

G, or | = 1, or both /

G< | < 1 and t#9 ≥

/

G.

By proving èêèJ≥ 0 and èê

èë≥ 0, we prove that èê

è2> 0. As dno9 > dpKK, we know

that {no9 |"# + 1 − | t# > {pKK(|"# + (1 − |)t#).

In sum, when | = 0, 1,/

G, we have {no9 |"# + 1 − | t# > {pKK(|"# + (1 −

|)t#) . When 0 < | </

G, by assuming that "#9 ≥

/

G, we have {no9 |"# + 1 −

| t# > {pKK(|"# + (1 − |)t#) . When /G< | < 1 , by assuming that t#9 ≥

/

G, we

have {no9 |"# + 1 − | t# > {pKK(|"# + (1 − |)t#).

B.2 Variances: We then compare, in a representative village, the elected and

appointed village leader’s variances of composite virtue-and-capacity. We know that

(B17) úùéno9 pKK |"# + 1 − | t#

= {no9(pKK) |"# + 1 − | t# G − {no9(pKK)G|"# + 1 − | t#

We first define û(Y à , â(à)) ≡ {no9(pKK) |"# + 1 − | t# G , and we have

(B18) û Y à , â à =}0B` /R} vB

@ }ä 0B ` /R} ä vB Å0BÅvB<Ä

<Ä

}ä 0B ` /R} ä vB Å0BÅvB<Ä

<Ä

where k "# = 1 − Y "#9 + Y"#, k t# = 1 − â t#

9 + ât#, Y ≡I>?@ 2

Iü>@ `I>?

@ 2, and â ≡

Iw?@ 2

Iyw@ `Iw?

@ 2.

First, we simplify the numerator of û ∙ as

(B19) |G"#G + 1 − | Gt#

G + 2| 1 − | "#t# ∙| 1 − Y "#

9 + Y"# + 1 − | 1 − â t#9 + ât# ì"#ìt#

/E

/E

� 53

=|î"#

G 1 − Y "#9 + Y"# + |G 1 − | "#

G 1 − â t#9 + ât#

+| 1 − | Gt#G 1 − Y "#

9 + Y"# + 1 − | ît#G 1 − â t#

9 + ât#+2|G 1 − | "#t# 1 − Y "#

9 + Y"# + 2| 1 − | G"#t# 1 − â t#9 + ât#

ì"#ìt#/

E

/

E

where

(B20) |î"#G 1 − Y "#9 + Y"# =

/

î|î 1 − Y "#

9 +/

ï|îY

(B21) |G 1 − | "#G 1 − â t#

9 + ât# =/

î|G 1 − | 1 − â t#

9 +/

†|G 1 − | â

(B22) | 1 − | Gt#G 1 − Y "#

9 + Y"# =/

î| 1 − | G 1 − Y "#

9 +/

†| 1 − | GY

(B23) 1 − | ît#G 1 − â t#

9 + ât# =/

î1 − | î 1 − â t#

9 +/

ï1 − | îâ

(B24) 2|G 1 − | "#t# 1 − Y "#9 + Y"# =

/

G|G 1 − | 1 − Y "#

9 +/

î|G 1 − | Y

(B25) 2| 1 − | G"#t# 1 − â t#9 + ât# =

/

G| 1 − | G 1 − â t#

9 +/

î| 1 − | Gâ

The numerator of û ∙ becomes /†| |G − | + 2 1 − Y "#

9 +/

†1 − | |G − | +

2 1 − â t#9 +

/

/G| |G + 2 Y +

/

/G1 − | |G − 2| + 3 â. Therefore, we have

(B26) û ∙ =<°} }@R}`G /RJ 0B

?`<°/R} }@R}`G /Rë vB

?`<<@} }@`G J`

<<@

/R} }@RG}`î ë

} /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë

Then we define á Y à , â à ≡ {no9(pKK) |"# + 1 − | t# , and we know that

á Y à , â à =<@} /RJ 0B

?`<@/R} /Rë vB

?`<<@} }`î J`

<<@

}Rï }R/ ë

} /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë

from (B14).

From (B17) we know that

(B27) 袣§ ∙

è2=

è• ∙

è2− 2á ∙ ∙

èê ∙

è2

It is known that á ∙ > 0,èê ∙

è2> 0. We then need to derive è• ∙

è2=

è• ∙

èJ∙èJ

è2+

è• ∙

èë∙

èë

è2. It is known that èJ

è2> 0,

èë

è2> 0, therefore, we

(B28) è• ∙

èJ=

<<@}ò0B

?`<<@} /R} @ë0B

?`<<@}@ /R} /Rë vB

?`<@ô} /R} G}R/ ë

[ /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë]@

(B29) è• ∙

èë=

<<@}@ /R} JvB

?`<<@

/R} òvB?`

<<@} /R} @ /RJ 0B

?`<@ô} /R} /RG} J

} /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë

@

Thus, è• ∙

è2=

<<@}ò0B

?`<<@} /R} @ë0B

?`<<@}@ /R} /Rë vB

?`<@ô} /R} G}R/ ë

} /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë

@ ∙èJ

è2

� 54

+<<@}@ /R} JvB

?`<<@

/R} òvB?`

<<@} /R} @ /RJ 0B

?`<@ô} /R} /RG} J

} /RJ 0B?` /R} /Rë vB

?`<@}J`

<@/R} ë

@ ∙èë

è2

It is easy to find that è• ∙

è2=

èê ∙

è2. In addition, from (B14) we could derive that

á ∙ >/

G, as twice the numerator of á ∙ is larger than the denominator of á ∙ . As a

result, we can derive from (B27) that 袣§ ∙

è2=

è• ∙

è2− 2á ∙ ∙

èê ∙

è2< 0. As dno9 >

dpKK, we know that úùéno9 |"# + 1 − | t# < úùépKK |"# + 1 − | t# .

C. Promotion Likelihood as the Village Party Secretary

We know that for the village leader’s composite virtue-and-capacity, the distribution

of the representative township official’s prior perception is m |G"¶ + (1 −

|)Gt¶, V0ßG + Vvß

G . After an update by observing her performance O = ℱ[(|" +

1 − | t)¢©] + ™, we can obtain the posterior distribution of village party secretary

candidate ´’s composite virtue-and-capacity. For simplicity, denote that U¶ ≡ |G"¶ +

(1 − |)Gt¶, U¢© ≡ (|" + 1 − | t)¢© and V¶G ≡ V0ßG + Vvß

G .

First, we derive ) U¢© , the density kernel of the prior distribution of composite

virtue-and-capacity. Since the prior distribution is a normal distribution truncated at

[0, 1], we have

(C1) ) U¢© = ) U¢© 0 ≤ U¢© ≤ 1, U¶)

∝9JK{

C ¨≠ÆC¨ß@

@=ß@ }

D H≠Æ EFH≠ÆF/,0B?)

where O U¢© 0 ≤ U¢© ≤ 1, U¶) = P(/RHß

Iß@ ) − P(

RHß

Iß@ ) represents the likelihood that

U¢© is at [0, 1], contingent on U¶.

Second, we derive the density of O as a likelihood function that

(C2) , U¢©; O ∝ XY! −dℱ[H≠Æ]RH≠Æ

@

GIØ@

Thirdly, by Bayes’ rule, the density kernel of posterior distribution of the village

leader’s composite virtue-and-capacity is

� 55

(C3) , U¢©; O ) U¢© ∝

9JK R<@[

<

=Ø@=ß

@

=Ø@i=ß

@

[H≠ÆR{=Ø@=ß

@

=Ø@i=ß

@<

=ß@H

ß`ℱ[¨≠Æ]

=Ø@ }]@]

D H≠Æ EFH≠ÆF/,Hß)

Therefore, this density kernel is still of a truncated normal distribution, in which

the posterior mean of the village leader’s composite virtue-and-capacity, which is also

her likelihood of being promoted as the village party secretary, is

(C4) s U¢©|O =IØ@Iß@

IØ@`Iß

@/

Iß@ U

¶ +ℱ[H≠Æ]

IØ@ =

IØ@

IØ@`Iß

@ U¶ +

Iß@

IØ@`Iß

@ ℱ[U¢©]