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Social Choice and Welfare

Erschienen in:

19.02.2022 | Original Paper

Voter conformism and inefficient policies

verfasst von: Cécile Aubert, Huihui Ding

Erschienen in: Social Choice and Welfare | Ausgabe 1/2022

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Abstract

A reelection-seeking politician makes a policy decision that can reveal her private information. This information bears on whether her political orientation and capabilities will be a good fit to future circumstances. We study how she may choose inappropriate policies to hide her information, even in the absence of specific conflicts of interests, and how voters’ conformism affects her incentives to do so. Conformism is independent from policies and from voters’ perceptions. Yet we identify a ‘conformism advantage’ for the incumbent that exists only when there is also an incumbency advantage. Conformism changes the incentives of the incumbent and favors the emergence of an efficient, separating equilibrium. It may even eliminate the pooling equilibrium (that can consist in inefficient persistence). Conformism has a mixed impact on social welfare however: it improves policy choices and the information available to independent voters, but fosters inefficient reelection in the face of a stronger opponent. When the incumbent is ‘altruistic’ and values social welfare even when not in power, she partly internalizes this latter effect. The impact of conformism is then non monotonous.

Vorheriger Artikel Compromise in combinatorial vote

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People who identify with the governing party perceive the results of economic policy more positively than subjects who identify with the opposition.

Many authors have confirmed the bandwagon effect, both empirically (Hodgson and Maloney 2013; Kiss and Simonovits 2014) and experimentally (Bischoff and Egbert 2013; Morton et al. 2015; Agranov et al. 2017).

Callander (2007) develops a model of sequential voting to argue that voters’ desire to win (by voting like most others do, and thus belonging to the majority) is critical to the existence of the bandwagon.

See Erikson (1971), Gelman and King (1990), Ansolabehere (2002), Ashworth and Mesquita (2008), Lee (2008), Hodler et al. (2010), Erikson and Titiunik (2015) and Fiva and Røhr (2018). The many causes of incumbency advantage include bureaucratic relations, pork barrel spending, campaign finances and practices (Ansolabehere et al. 2006), and the structure of intra-party competition (Ansolabehere et al. 2007). Holding office helps incumbents obtain more media coverage (Prior 2006) and additional financial support for their campaigns (Gerber 1998).

See Levitt and Wolfram (1997), Trounstine (2011) and Snyder et al. (2015). Levitt and Wolfram (1997) report that incumbents can achieve reelection rates of around 90%. Lee (2008) shows that in Congressional elections, a party which wins with a small number of additional votes in a very close election (suggesting that the electorate is very balanced between the party and its opponent) has a 35% higher probability of winning the next election.

For convenience, we refer to a politician as ‘she’ and to a voter as ‘he’.

“COVID-19 has changed the tenor of the election in unmistakable ways. [...] The pandemic has brought new urgency to issues like access to health care, inequality and the social safety net, while driving Trump’s preferred topics of immigration and trade out of the picture” [...] “Biden’s strengths suddenly seem matched to the moment”. (Time magazine, August 17, 2020).

Surveys indicate that Republicans have consistently been less likely than Democrats to say that they fear being hospitalized because of COVID-19 or that they might unknowingly spread the virus to others (Pew Research Center 2020). This partisan gap has widened significantly between April and June 2020. Importantly, Republicans are also more likely to say they think the worst is behind us. Here also, the difference with Democrats has widened.

“Trump’s campaign insists he is positioned for victory despite the headwinds. Public polls are undercounting Republicans, says Miller, the Trump political adviser, and the President’s supporters are more enthusiastic about voting by a 2-to-1 ratio” (Time magazine, August 17, 2020).

In economics, Zafar (2011) experimentally highlights that informative conformity matters for decision-making, in the shape of learning about the descriptive norm (i.e., what others are doing). Grodner and Kniesner (2006) study the effect of normative conformity on wages and labor supply. Ding (2017) models normative conformity as the desire to vote like the majority when voting on collective decision-making under the unanimity rule. Pivato (2017) develops a theory of epistemic democracy with correlated voters where the voters influence one another via a social network, because of normative conformity.

Signals are perfectly reliable, so the prior on signals is also the prior over states.

If the incumbent was instead from a party more favorable to interventionism, the labels a, b, A and B would have to be inverted.

The expected benefit can be interpreted as the probability that the incumbent will make decisions leading to a benefit of 1, rather than 0, if she is reelected.

Because the voters’ perceptions of the incumbent’s quality can be shaped by many observations pertaining to her first mandate, which is not the case for the challenger, perceptions about their ability need not follow the same distribution.

We use the same letter, \(\mu\), for all beliefs about politicians’ ability. However it should be clear that the revised beliefs of players depend on their information: the signal s for the incumbent, the decision d taken by the incumbent for the voters. Beliefs about the opponent, \(\mu ^o\), are exogenous from the point of view of the players.

The desire to pick the winner should not systematically override the desire to achieve good policies. To avoid dealing with multiple conditions (to ensure that this is true for all configurations), we adopt a representative voter. The literature on voter turnout has often used the concept of the quasi-symmetric mixed-strategy Nash equilibrium in which voters in favor of the same alternative use the same strategy. In our specific context, this boils down to a representative voter. Media coverage, opinion polls and political advertising can serve as coordination devices.

To simplify mathematical expressions, we assume that the opponent can never win without the independent vote. The analysis could be extended to the more general case in which her probability of wining without support from the independent voter is lower than the corresponding probability (p) for the incumbent.

If \(\Omega < 0\), the incumbent is confrontational and wants her opponent to fail when in power, possibly because this will affect other election outcomes, or due to strongly divergent values. We do not discuss this case here as it does not provide interesting additional insights: Being confrontational reinforces the desire to be re-elected. Computations for this case are available from the authors upon request.

There is no abstention (Callander 2008). If there is a tie, the winner is the opponent. We assume that there is no discount factor for simplicity.

We use a slightly different way of denoting these values, compared with the a posteriori belief \(\mu ^E(d)\), on purpose, to help visually differentiate them.

In the seminal signaling model by Spence (1973), applying the Intuitive Criterion eliminates all pandering equilibria. This is not the case in our context because the Spence - Mirrlees, ‘sorting’ condition is not met for all parameter configurations. The a-type gets a higher utility, if elected, than a b-type; However making decision A can, or not, provide a higher gain to a b-type incumbent, via: the increase in re-election probability. So the two types of incumbents may not be ‘sorted’ according to the strength of their incentive to make decision A rather than B. This is why the Intuitive Criterion selects among possible out-of-equilibrium beliefs in a pooling equilibrium but does not eliminate this type of equilibrium.

One needs simply to replace \(\mu ^P(B)\) by \(\mu ^{ooe}\) in formulas that relate to the P equilibrium. This creates only quantitative changes, except for the equality between two sets of parameters, where the impact of our assumption is discussed in the text. Assuming \(\mu ^{ooe} = \mu\) corresponds to the assumption of ’passive beliefs’, which is frequent in a number of games but unrealistic in ours: The negative impact on voters’ beliefs associated to a given policy (here B) is indeed the crucial reason why the incumbent may consider a pooling equilibrium in the first place. We show below how assuming passive beliefs would destroy the incentive to pander.

Note that in case S3, \(W < \frac{1-p}{p}(1-\mu ^{a})\), which implies that \(\mu ^a - \mu ^b > 1 - \mu ^b - \frac{pW}{1-p}\): The condition for the incentive constraint to be met is stricter than if it remained the same as in case S2.

Before simplification the condition writes as: \((X_1 + 1)+ p(X_2 +\mu ^{a}) +(1-p)[G(\hat{\mu })(X_2 + \mu ^{a})] \ge (X_1+0) + p(X_2 + \mu ^{a}) +(1-p)[G(\hat{\mu }^{S}(B))(X_2 + \mu ^{a})].\)

When beliefs do not react to the incumbent’s decision, \(\hat{\mu }^{SB}\) has to be replaced by \(\hat{\mu }\). The right-hand side becomes null (\(G(\hat{\mu }) - G(\hat{\mu }) = 0\)), and we cannot have \(\frac{L}{1-p} \le 0\). Choosing the ‘bad news’ policy B does not degrade beliefs (nor reelection chances); but it enables to avoid the loss L due to a non congruent policy. It is therefore always a better strategy. In other words, if we assumed passive beliefs, the negative signal associated to policy B would be assumed away, and the pandering equilibrium P could not exist.

If the incumbent played the out-of-equilibrium strategy B, the threshold would be determined by the out-of-equilibrium beliefs, and equal to \(\frac{1-p}{p}(1 -\mu ^{ooe})\) given our assumption that \(\mu ^S(B) = \mu ^{ooe}\).

Condition \((IC)^P_{\Omega =0}\) is then equivalent to \(L \le 0\), which is not possible.

With out-of-equilibrium beliefs \(\mu ^{ooe}\) when policy B is chosen, the S equilibrium is the only pure-strategy equilibrium that exists when \(W \ge \frac{1-p}{p}[1-\mu ^{ooe}]\).

For strong conformism (S1), the incumbent is always reelected and generates an expected welfare that depends on the signal. For intermediate conformism (S2), she is reelected for sure when \(s=a\) as she then plays A, but not always when \(s=b\) (as she then plays B) in which case the opponent gets reelected with a positive probability and creates expected welfare \(\frac{1 +\hat{\mu }:^{SB}}{2}\). For weak conformism (S3), reelection is always uncertain.

In some cases, one may argue that in a long-term perspective and for very ideological elections, an incumbent may want her opponent to fail in her choices, so as to ensure that the incumbent’s party will be back in power in a future period. We abstract from this last case (\(\Omega < 0\)).

Conversely an altruistic incumbent may have perverse incentives to select B while her signal is a, in order to reduce her reelection chances despite a strong desire for conformity from voters. However it seems reasonable to assume that parameters are such that the associated incentive constraint is not relevant.

\(SW(S1) - SW(S2) = (1-\mu )\left( 1 - (p + (1-p)(\mu ^b +\frac{p}{1-p}W)\right) \frac{1}{2}(1-\mu ^b -\frac{p}{1-p}W) <0\).

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Titel: Voter conformism and inefficient policies
verfasst von: Cécile Aubert
Huihui Ding
Publikationsdatum: 19.02.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 1/2022
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-022-01391-w

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