Costly Advice. Mehmet Ekmekci and Stephan Lauermann. August 31, 2017

Transcription

1 Costly Advice Mehmet Ekmekci and Stephan Lauermann August 31, 2017 Extended abstract consisting of an introduction that describes our results and a discussion of the literature relation. Abstract We study a scenario in which a receiver is collecting non-binding advice for a binary decision from partially informed senders who can send binary messages. This reects situations such as non-binding voting of shareholders on a mangement proposal. Under complete information, the preferences of the receiver and the senders are aligned but there is a conict of interest over the trade-o of Type I and Type II errors. Existing work shows that for many such situations, the bias prohibits the transmission of any information. Here, in contrast to this work, we consider a setting in which one of the messages is costly. For example, there are positive costs of voting but no costs of abstention. We show that informative advice is given in any equilibrium. When there are many senders, with costly advice, the outcome is equivalent to the one under complete information. Keywords: Information Aggregation, Non-binding Voting, Shareholder Voting, Costly Voting. We are grateful for comments from Nadya Malenko and Andrey Malenko. This work was supported by a grant from the European Research Council (ERC ). Boston College, 140 Commonwealth Ave., Chestnut Hill, MA ekmekci@bc.edu. University of Bonn, Department of Economics, address. s.lauermann@uni-bonn.de.

2 1 Introduction Receiving advice is ubiquitous: Decision makers often rely on the information of a group of individuals to learn about an unknown state of the world which determines the best course of action. For example: 1. The board of a rm holds a non-binding vote among the shareholders to decide whether to approve a proposal to change the operations of a rm, a takeover decision, expansion plans or executive compensation packages. 2. A policy-maker decides whether to change a policy based on the petitions signed by the citizens or based on the protest activity. For example, in Japan, community union members' protest activity aects judge's decisions Kandori and Obayashi (2014), universities occasionally change the commencement speaker based on student protests. 1 Republicans changed their minds about elimination of a nonpartisan investigative body called the Oce of Congressional Ethics, due to a barrage of phone calls from citizens. 2 Many other examples are also provided in Battaglini (Forthcoming). 3. A manager holds a survey among the employees to learn about the future prospects of launching a new product, or eectiveness of a marketing strategy. 4. A policy maker organizes polls to elicit citizens' information regarding current policies (some presidents of US and other nations regularly do this, like Nixon, Erdogan, for more examples, see Morgan and Stocken (2008)) In all these situations, dispersed information across a group of experts is elicited through a procedure that resembles a voting process, since the message space is restricted to a limited number of options through which the experts can express their opinion. In a poll, the options are approving a policy or not, in a company survey, the options are supporting a new product launch or not, in a protest, the options are participating in a protest or not, or deciding which one of multiple protests to participate, in a shareholder voting, the options are whether to approve a say-on-pay or a golden parachute compensation plan or not. In all these examples, unlike in a referendum or in elections, the decision maker does not commit to a voting rule ex-ante, hence the vote is just a recommendation to the decision-maker. 1 International Monetary Fund chief Christine Lagarde withdrew from Smith College's commencement ceremony after protests from students over the IMF's meddling approach to foreign aid. Condoleezza Rice, tapped to deliver the commencement address at Rutgers University, stepped down after criticism coalesced around her role in the Iraq War. And Brandeis University cancelled plans to award American Enterprise Institute fellow Ayaan Hirsi Ali an honorary degree at commencement after students raised concerns about statements she's made that are critical of Islam. 2 See 1

3 This feature distinguishes our environment from the voting environment in which the rule the decision maker uses to implement a policy is xed before the game. We explore the eectiveness of such procedures to elicit information from the experts when reporting information is costly. As shown in previous work (see Proposition 13 of Morgan and Stocken (2008), Levit and Malenko (2011) and Battaglini (Forthcoming)) in such an environment, if voting is costless, then no information transmission is possible if the decision-maker and the voters' preferences are suciently diverse from each other, or if each expert's information is poorly informative. We show that if voting is costly, then information transmission is possible, and if the pool of experts is large, information aggregates, i.e., there is an equilibrium in which the decision-maker makes the right decision in both states of the worlds, regardless of the precision of experts' information or the magnitude of the conict of interest between the experts and the decision-maker. Our nding that voting costs help information transmission and aggregation suggests that making voting mandatory instead of voluntary may render non-binding voting as an ineective information transmission mechanism (see Krishna and Morgan (2012) for a similar suggestion when voting rule is xed and is majority voting rule). Indeed, there is a recent discussion about an SEC ruling which was enacted in 2011 as part of the Dodd-Frank- Act, that requires all publicly traded companies to have a non-binding vote on executive compensation (so called "say-on-pay" proposals) and golden parachute compensation. 3 Such proposals are the most common issue that has non-binding voting (more than 2000 votes a year) and received a lot of attention from institutional investors, which led to a rise in proxy advising activity (see Malenko and Malenko (2016) for a more detailed discussion of the role of proxy advisors). Although voting in such proposals was not mandatory, it was perceived to be as such among the institutional investors. In 2014, SEC issued SEC's Sta Legal Bulletin No.20 (SLB 20), which provided guidance for investment advisors' use of proxy advisors: ( The answer to Question 2 in SLB 20 was aimed to emphasize that institutions are not required to vote for all issues. 4 In light of our result, the issuance of SLB 20 to clarify that such non-binding votes are voluntary can 3 See, 4 For example, a law article that discusses the interpretation of SLB 20 is: See : "A key point emphasized in SLB 20 is that the Proxy Voting Rule does not require that investment advisers vote every proxy or take on all of a client's proxy voting responsibilities. Although the SEC had previously conveyed this message in other materials, many investment managers interpreted two 2004 no-action letters to indicate that they were required to vote on all matters. This interpretation led to heavy reliance on proxy advisory rms, as investment advisers largely outsourced their voting responsibilities. The recent guidance refutes this interpretation and suggests a variety of arrangements in which a client and an investment adviser may allocate the proxy voting responsibilities between them as dictated by the best interests of the client. 2

4 be explained as an attempt to facilitate information transmission and aggregation through (voluntary) non-binding voting. Suppose a decision-maker needs to choose one of two policies, A or B, and policy A is the right choice in state α and policy B is the right choice in state β. There is a pool of experts who are privately and imperfectly informed about the state of the world. Each expert after observing their cost and information chooses whether to abstain or pay their voting cost and sends a message to the decision-maker. Such a message in the protest model proposed by Battaglini (Forthcoming) is participation in a protest. In the non-binding shareholder voting model proposed by Levit and Malenko (2011) and in the model of polls proposed by Morgan and Stocken (2008) there are two messages, A or B. The decision-maker, after observing the vote outcome (or size of the protest) makes a decision. The experts and the decision-maker fully agree on the right decision in each state of the world, but they dier in their relative values of making the right choice and the wrong choice in each state of the world (i.e., on the tradeo between type I and type II errors in the decision). In particular, suppose the experts prefer A to be implemented if they believe the state is α with probability more than 1 2 whereas the decision-maker prefers policy A when his belief attaches probability at least µ > 1 to state α. The dierence between 2 µ and 1 measures the conict of interest between 2 the experts and the decision-maker. Previous work has shown that if the conict of interest between the decision maker and the experts is suciently big, or if the precision of the experts' information is small, then no information can be transmitted through non-binding voting (see Battaglini (Forthcoming) in the context of protests, Levit and Malenko (2011) in the context of shareholder voting and Proposition 13 of Morgan and Stocken (2008) in the context of polls), if reporting is costless. This suggests that non-binding voting may not be an eective way to elicit advice from a group of experts, citizens or shareholders. We nd that when there are arbitrarily small costs of reporting: 1. Information transmission is possible 2. If the size of the pool of experts is large, then information aggregates, i.e., the decision maker makes the right choice in each state. Our results don't depend on the magnitude of the conict of interest, nor the precision of signals, and only require that experts' signals are informative and dispersed. The key assumption that delivers our result is that each voter's cost from voting, c is drawn from a distribution F ( ) with positive density at 0, i.e., there are voters with positive but arbitrarily small costs. 3

5 To see why costly voting helps, consider a one-sided voting model in which an expert has only two choices, abstain or participate in a protest. Suppose the experts receive a binary signal, a and b that are indicative of states α and β, respectively. Suppose also that the experts are poorly informed, i.e., the signals are not very informative about the state of the world. Suppose rst that participation in the protest is costless. An expert's participation changes the decision maker's decision, i.e. the expert is pivotal, only when the decision maker's belief without an additional participating expert is smaller than µ, and with the additional expert, his belief is above µ. Because the experts are poorly informed, when an expert is pivotal, the probability that the state is α is close to µ. Therefore, conditional on being pivotal and his own signal, an expert thinks the state is α with probability more than 1 regardless of the realization of his signal, and hence expert's participation decision 2 is signal independent. Hence, there is no information transmission in equilibrium in this case. Suppose now that experts incur participation costs as described above. Conditional on being pivotal, an expert with an a signal believes the state is α with a probability that is strictly higher than the belief of an expert with a b signal. Hence, the cost that an expert with an a signal is willing to incur to participate is strictly higher than the cost that an expert with a b signal is willing to incur. This induces participation rates that are signal dependent, hence participation size is informative about the state of the world. Costly voting allows screening of experts with dierent signals that is not possible when voting is costless. For our information aggregation result with a large pool of experts, we need that it is possible that the cost is arbitrarily small, but not 0 (that is, F ( ) continuous at 0, and f(0) > 0). This is because, if number of participants grows without bound the pivot probability goes to zero, and no expert votes if the costs are bounded away from zero. Therefore, when costs are bounded away from zero the expected number of participants is bounded, hence information is not fully aggregated (This is a familiar argument from Downs (1957)). Although the intuition described above is appealing, it does not rule out the possibility that such an equilibrium doesn't exist to start with, or that as the pool of experts grows without bound, the participation rates of dierent signals converge to each other, and the information contained in a participation decision disappears. Our analysis shows that responsive equilibria in which there is some participation and that transmits information exists, and that when the expert pool grows large, the decision-maker makes the right choice. In an important extension of our model, we assume that a fraction r [0, 1] of the experts either have no cost of participation (i.e, F (0) > 0), or get a positive benet from participation. In the latter case, in equilibrium, these experts participate independent of their signal. 4

6 Therefore, they can be interpreted as extremists who participate in protests regardless of their information. Such citizens add signicant noise to the information transmission process.when r = 1, and when the experts have no cost of participation, this model becomes Battaglini's model with binary signals. We show that when r < 1, if f(0) is suciently large, then information transmission is possible. Dierent from our benchmark model, information contained in a participation decision disappears as the size of the expert pool grows. Moreover, if f(0) is bounded, then type-i and type-ii errors remain in the limit, yet there is still non-negligible amount of information transmission in the limit. We calculate the exact limiting amount of information transmitted, and show that if the fraction of noise voters, r, is close to 0, or if f(0) is large, then type-i and type-ii errors are small. Strikingly, if f(0) =, and if a minor technical condition on F ( ) holds, we show that for any r < 1 information aggregates, i.e., decision-maker's decision is correct with a probability that approaches 1 as the size of the expert pool grows. Our assumption that f(0) > 0 allows the noise from the costs to disappear when the pool of experts is large. When there are extremists (as in explained in the above paragraph), hence preference heterogeneity, then costs also help lter out the noise introduced from these voters' behavior, partially so if f(0) <, and completely if f(0) =. The key is that the voting incentives are signal dependent in our model, hence variation of such incentives among dierent voter types help information transmission. In order to facilitate analysis of shareholder voting, surveys, polls and multiple protests, we introduce a two-sided voting model which in which citizens can participate in voting, and they can choose one of two options, support policy A or support policy B. In the nonbinding shareholder voting example, this corresponds to a choice of whether to approve or disapprove a compensation package (see Levit and Malenko (2011)). In the protest example, whether to join a protest in favor of a policy or against a policy when multiple types of protests are possible. 5 In a survey by a manager, or a poll organized by a president, this corresponds to how to respond to the questions in the poll (see Morgan and Stocken (2008)). We observe that this model admits equilibria of the one-sided voting model, since decisionmaker and the voters can mutually ignore one of the voting options. Therefore, it trivially follows that information transmission and aggregation is possible when voting is costly. Interestingly, when experts' signals are poorly informative or when the conict of interest is suciently large, then there is no equilibrium in which expected number of votes for both options is positive. When we introduce preference heterogeneity among the shareholders, equilibria where expected number of votes for each option is positive exists. We show that such equilibria aggregate information when the pool of experts grows without bound. This 5 In Germany, right-wing protests are often accompanied by a left-wing protest. 5

7 contrasts with the case of in which voting is costless, where there is no information transmitted in any equilibrium for any size of expert pool, when the conict of interest between the decision-maker and the voters is suciently large, or when the experts are poorly informed (see Levit and Malenko (2011)). Our main hypothesis is that experts, citizens or shareholders incur arbitrarily small costs of voting or participation. Existence of participation or voting costs is clear. Randomness and possibly arbitrary smallness of costs (f(0) > 0) however is not always an innocent assumption. In shareholder voting, participation is easy especially with online voting suggesting that cost of voting is small. In protests, there are possibly large costs, due to possible imprisonment or tear gas by police, 6 yet with online petitions the cost of signing a petition is arguably small. In surveys and polls also the time it takes to respond varies between less than a minute to half an hour. Likewise, boycotts of certain department stores or products as a form of protest also incurs a cost, and the magnitude varies across the population from very small to possibly big costs, justifying or assumption that voting costs are random, and arbitrarily small for some voters. 2 Related Literature Our paper is most closely related to the recent work on communication between multiple senders and a receiver where the message space is restricted. These models resemble a voting process in which the receiver does not commit to a particular voting rule ex-ante. Morgan and Stocken (2008) study a model of polling in which the receiver chooses a policy from a continuum of possible policies after seeing the results of a poll obtained from a group of experts with heterogenous preferences and with dispersed information. They show in Proposition 13 that when there is a conict of interest between the policy-maker and the experts, the amount of information transmitted is limited regardless of the size of the expert pool. in our model, the policy-maker has a binary policy choice, and when voting is costless, a similar conclusion holds. Levit and Malenko (2011) model non-binding shareholder voting where the board and the shareholders have a conict of interest, and show that when the conict is suciently large, the unique equilibrium is babbling. In their model the number of shareholders is deterministic whereas in our model the population size is Poisson distributed. 7 Moreover, we allow for preference heterogeneity in our model. Battaglini 6 In January 2016, 1128 academics in Turkey signed a petition condemning Turkish government's operation in south east Turkey based on its damage on the civilians in that area. Three academics who signed the peace petition have been jailed by an Istanbul court on allegations of making terrorist propaganda. At least 30 other academics have been dismissed and 27 suspended by their universities pending investigation. (see or 7 Typically, in voting models assuming deterministic population size versus uncertain population size with Poisson distribution doesn't change the qualitative results. See for instance Myerson (1998a,b, 2000). In our 6

8 (Forthcoming) proposed a similar model where population size is Poisson distributed to study public protests, and arrived at a similar conclusion. 8 Dierent from the above mentioned papers, other than some minor technical modeling dierences, we study the eect of costly communication, and show costs help information transmission and aggregation regardless of the precision of experts' signals and the size of the conict of interest. Our results highlight that non-binding voting may be an eective way to elicit dispersed information when participation or voting is costly, and when voting is voluntary. There are other means proposed by previous work that facilitates information transmission and aggregation in such environments. Battaglini (Forthcoming) suggests communication via social media may facilitate information aggregation by increasing the precision of signals among groups, Morgan and Stocken (2008) argue existence of citizens with suciently small conicts of interest with the decision-maker facilitate information aggregation, and Levit and Malenko (2011) suggest existence of an additional third party who can pressure the decision-maker for not following the advice of the shareholders may facilitate information aggregation. Our analysis complements all these other proposed solutions, and oers a simple and new channel by which costly voting may increase eciency and information aggregation. Information aggregation through voting mechanisms in which the voting rule is xed ex-ante has been studied extensively. Notably, Austen-Smith and Banks (1996) showed that sincere voting is typically not consistent with rational behavior, and Feddersen and Pesendorfer (1997) showed that under any super-majority voting rule except unanimity, large elections aggregate information. In these models voting is costless. In a series of more related work, Krishna and Morgan (2012, 2011, 2015) studied the role of voting costs and compared voluntary voting versus mandatory voting when the voting rule is xed. Krishna and Morgan (2015) shows in a complete information setup where voting rule is a supermajority rule, voluntary voting results in the utilitarian outcome in large elections only when the voting rule is majority rule. Krishna and Morgan (2012) shows in a pure common value model with majority voting that voluntary voting induces sincere voting and information aggregates in large elections. In their model information aggregates when voting is compulsory, or when there are no voting costs (see also McLennan (1998) for this conclusion). Therefore, voluntary voting economizes on the costs of voting, and hence is welfare superior to mandatory voting. 9 Krishna and Morgan (2011) shows in a model with model also Poisson distributed population size makes calculations easier, but our results don't depend on this modeling choice. 8 Yildirim (2012) also observed that not all voting rules are ex-post optimal, hence there are voting rules for which a decision-maker would have incentives to renege on the outcome of the voting process. 9 This paper also shows that when the electorate size is small, voluntray voting is still strictly superior to 7

9 both private and common values that majority voting with voluntary voting results in the utilitarian outcome state by state. All of these models share the feature that costs induce a certain type of sorting of dierent voter types at the participation stage, hence allows the preference intensities to be reected in the participation decision. Our model also shares this feature. However, in our model where voting rule is not xed ex-ante, the sorting costs induce at the participation stage allows information transmission compared to the benchmark case of costless voting in which for some parameters there is no information transmission. In the above mentioned papers, costly voting either helps select utilitarian outcome instead of the median voter's choice when voting rule is majoritarian, or induces sincere voting under some restrictions on the signal precisions. 10 Our framework is an example of a sender-receiver game, rst modeled by Crawford and Sobel (1982) with a single sender. They show that communication is limited because of dierences of preferences between the sender and the receiver. Austen-Smith (1990, 1993) study models where there are multiple senders and the receiver does not commit to a voting rule ex-ante. These papers focus however on the case when the number of senders is small, and there is no cost of communication. 11 Other related papers on polling are Lohmann (1993), Banerjee and Somanathan (2001), and Cukierman (1991) and McKelvey and Ordeshook (1985). mandatory voting in welfare. 10 Costly voting has been extensively studied: Ledyard (1984) showed that even when there are costs of voting, turnout is positive. Relatedly, Palfrey and Rosenthal (1983, 1985), Myerson (2000) study also costly voting. Borgers (2004) shows in a symmetric environment that voluntary voting economizes on voting costs, Krasa and Polborn (2009) shows that when the symmetry assumption is dispensed with, then mandatory voting may be better for the voters. Ghosal and Lockwood (2009) shows via an example that when there is a common value component, mandatory voting may be superior to voluntary voting.. Taylor and Yildirim (2010) shows that costly voting leads to the underdog aect. Feddersen and Pesendorfer (1996) and Feddersen and Pesendorfer (1999) analyze models in which voting is costless and show swing voter's curse, and show that less informed voters abstain when voting is voluntary. 11 See also Battaglini and Benabou (2003); Battaglini et al. (2004) on the related topic. Likewise, there is a literature on cheap-talk with multiple senders, and in this literature it is typically assumed that the senders's information is not dispersed, see Battaglini (2002) for instance. 8

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12 Yildirim, H. (2012): Time-Consistent Majority Rules with Interdependent Valuations,. 11