A summary of Theory and Evidence on the role of social Norms in Voting by Patricia Funk Omer Ali

1
A summary ofTheory and Evidence on the role of
social Norms in Voting by Patricia FunkOmer Ali
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Contents

• Overview
• Model
• Empirical Evidence
• Comparison of results
• Conclusions

3
Overview

• Motivation
• Key question Does social pressure (perception of
  a good citizen) influence decision to vote?

4
Overview

• Investigation of social norm incentives for
  voting (being seen in the act of voting)
• Method of investigation
• Model
• voting as a signal of a citizens type
• survey evidence in Knack (1992) and Opp (2001)
  suggests that citizens with a strong sense of
  civic duty are more likely to vote
• Empirical evidence
• Switzerlands staggered introduction of postal
  voting

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The Model

• Benefits of norm adherence introduced to
  classical model of voting
• Net benefit from voting R pB E C
• E can be defined as internal benefits
  signalling benefits, for example
• social esteem
• avoidance of informal sanctions
• more cooperative trades with other citizens

6
The Model

• Two types of citizens
• Proportion (a) are co-operators who care about
  voting, their payoff is
• R pB D S C
• Proportion (1 a) are defectors who dont care
  about voting but value signalling benefits
• R pB S C
• Where D is a civic duty (warm glow) benefit from
  voting and S is the signalling benefit discussed
  earlier.

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The Model

• The signalling game
• A citizen (player 1) sends a signal by voting or
  not voting
• Assume that all citizens (regardless of type) get
  equal payoff from giving esteem
• Citizens can be characterised by a
  representative receiver (player 2)
• A representative receiver wants to give esteem
  only to a co-operator who votes

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The Model

• Variables
• Signalling benefits S Vng
• V value of being esteemed by a citizen
• n number of people met at the voting booth
• g gossip (greater than or equal to 1)
• s community size
• g 1/s
• S Vn/s
• Let v Vn, then S v/s

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The Model

• The signalling game

v/s, 0
v/s C, 0
e
e
Defector
(1 p)
(1 q)
NV
V
ne
C, 1
0,1
ne
(1 a)
Receiver
Receiver
v/s D C, H
v/s, 0
e
(a)
e
NV
V
(p)
(q)
Co-operator
ne
0,1
D C, H
ne
Note H gt 1
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The Model

• Results, given a gt 1/(12H) and C gt D
• Pooling equilibrium for small communities (slts1)
  where everyone votes
• Separating equilibrium for medium-sized
  communities (s1ltslts2, when v/s lt C) where
  co-operators vote and defectors do not
• Pooling equilibrium for large communities (sgts2)
  where no-one votes

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The Model

• Results, given a gt 1/(12H) and C gt D

benefits/costs fromvoting
voter turnout ()
100
a
C
v/s D
v/s
s1
s2
community size
s1
s2
community size
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The Model

• Results, given a gt 1/(12H) and C gt D
• Non-positive relationship between community size
  and voter turnout
• Signalling benefits from voting will motivate
  defectors to vote i.e. there is a social pressure
  to vote

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The Model

• Consider a community with modern voting tools
  (e.g. postal voting)
• Citizens have a choice of either voting at the
  polls (PV) or voting by mail (MV)
• Voting by mail costs a citizen c lt C (C is cost
  of voting at the polls)
• Assume that D gt c and co-operators always vote

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The Model

• Community with modern voting tools

v/s c, 0
e
v/s C, 0
e
MV
Defector
(1 p)
(1 q)
- c,1
ne
NPV
PV
v/s, 0
e
C, 1
ne
NMV
(1 a)
ne
0,1
dominant strategies
v/s D c, H
e
v/s D C, H
e
(a)
MV
ne
D c, H
v/s, 0
NPV
PV
(p)
(q)
e
Co-operator
NMV
ne
D C, H
ne
0,1
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The Model

• NMV dominates MV for a defector
• i.e. a defector not voting at the polls never
  votes by mail
• MV dominates NMV for a co-operator
• i.e. a co-operator not voting at the polls always
  votes by mail
• Receivers have a publicly known prior belief (d)
  about the proportion of co-operators voting by
  mail.

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The Model

• Results

voter turnout ()
voter turnout ()
d gt (1 a)/(a.2H)
d lt (1 a)/(a.2H)
100
100
a
a
s1
s2
community size
community size
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The Model

• Results
• Non-positive impact on equilibrium voter turnout
  in small communities
• Non-negative impact on equilibrium voter turnout
  in large communities

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Empirical Evidence

• Switzerland
• Population 7 million
• 26 major districts (Cantons)
• Legislatively autonomous
• Some introduced optional mail voting in 1980s
• Some did so in 1990s
• Minor districts (communities) within Cantons
• Swiss voting process
• Every eligible citizen receives ballot by mail
• If postal voting allowed, return envelope is
  provided
• If not, citizen delivers ballot to polling station

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Empirical Evidence

• Aims of empirical study
• Analyze the effect of the introduction of
  optional postal voting on aggregate voter turnout
• Check if this effect is the same for communities
  of different sizes
• Method
• Cantons introducing optional postal voting at
  different times allows the use of
  difference-in-difference estimation

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Empirical Evidence

• Econometric models
• VTst is voter turnout () in Canton s in election
  t
• Dummy variable (Postal) takes a value of 1 if
  postal voting is offered and 0 otherwise
• In the second specification, (prop) is the
  proportion of cantonal residents living in small
  communities (i.e. lt 1000 inhabitants)

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Empirical Evidence

• Z denotes control variables
• Population (per Canton per year)
• Age (proportion in different age classes)
• Higher education (number of high school degrees
  per 15-19 year-olds)
• Unemployment Rate
• Income (average per capita)
• prop living in very small communities (lt1000
  inhabitants)
• Duty whether or not a Canton has a fine for
  non-voting

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Empirical Evidence

• Results
• Coefficient on (Postal) is not significant,
  meaning the introduction of postal voting did
  not increase turnout.
• Negative coefficient on (Postal.prop), meaning
  Cantons with a higher proportion living in small
  communities witnessed a more negative effect on
  turnout

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Empirical Evidence

• Further investigation of community-specific
  effects
• Community level data from Canton Zuerich
• 171 communities (gt20 very small)
• Introduced postal voting in 1994
• Control group Canton St Gallen (neighbour)
• 86 communities (10 very small)
• Introduced postal voting in 1979
• Similar in culture, language and politics

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Empirical Evidence

• Overview of data
• Graphs show voter turnout before (1st graph) and
  after (2nd graph) the introduction of postal
  voting in Canton Zuerich
• Relatively clear that there was a general drop
• Larger drop in voter turnout in smaller
  communities?

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Empirical Evidence

• Econometric models (run separately for Zuerich
  and St. Gallen)
• VTct is voter turnout () in community c in
  election t
• b1 measures the average impact of postal voting
  on turnout
• Postal.Small takes a value of 1 if postal voting
  is allowed and the community has lt 1000
  inhabitants
• Postal.Big takes a value of 1 if postal voting is
  allowed and the community has gt 1000 inhabitants
• Z (control variables) similar to previous model

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Empirical Evidence

• Community-specific results
• Highly significant coefficients on Postal suggest
  that turnout drops 5 due to postal voting
• Highly significant coefficients on Postal.Small
  and Postal.Big confirm result that turnout drops
  more in small communities due to postal voting

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Comparison of results

• Pivotal voter model
• Reduction in cost (c to c)
• Decreases turnout if turnout was initially high
• Increases turnout if turnout was initially low
• Increase in community size (M to M)
• Decreases turnout if turnout initially low
• Increases turnout if turnout initially high

q
q probability that a player chooses to vote
(turnout) p probability of being pivotal M
community size c cost of voting
pf(q,M)
qH
pf(q,M)
qL
2c
2c
pf(q,M)
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Comparison of results

• Pivotal voter model with incomplete info
• Costs unknown, normally distributed in interval
  0,1
• Increase in community size (M to M) decreases
  turnout

q
Distribution function F(c)
f(q,M)
f(q,M)
C(q)
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Comparison of results

• The swing voters curse
• Less informed voters have an incentive to abstain
  from voting.
• In large elections, an increase in the number of
  informed voters leads to higher participation.

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Conclusions

• Pivotal Voter model
• Agrees with community-level data in small
  communities (with high turnout), a reduction in
  costs decreases turnout but not vice versa
• Doesnt fit the data with respect to an increase
  in community size
• Pivotal Voter with incomplete info
• Agrees with community-level data for Canton
  Zuerich as community size increases, voter
  turnout decreases
• Swing Voters curse
• Unable to test results because data on
  information of voters is required