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Book: Storable Votes: Protecting the Minority Voice

"Storable Votes and Agenda Order Control. Theory and Experiments"
The paper studies a voting scheme where members of a committee voting sequentially on a known series of binary proposals are each granted a single extra bonus vote to cast as desired - a streamlined version of Storable Votes. When the order of the agenda is exogenous, a simple sufficient condition guarantees the existence of welfare gains, relative to simple majority voting. But if one of the voters controls the order of the agenda, does the scheme become less efficient? The endogeneity of the agenda gives rise to a cheap talk game, where the chair can use the order of proposals to transmit information about his priorities. The game has multiple equilibria, differing systematically in the precision of the information transmitted. The chair can indeed benefit, but the aggregate welfare effects are of ambiguous sign and very small in all parameterizations studied. The theoretical conclusions are tested through laboratory experiments. Subjects have difficulty identifying the informative strategies, and tend to cast the bonus vote on their highest intensity proposal. As a result, realized payoffs are effectively identical to what they would be if the agenda were exogenous. The bonus vote matters; the chair's control of the agenda does not.

"Protecting Minorities in Binary Elections. A Test of Storable Votes Using Field Data"
with Shuky Ehrenberg, Andrew Gelman and Jie Shen

Democratic systems are built, with good reason, on majoritarian principles, but their legitimacy requires the protection of strongly held minority preferences. The challenge is to do so while treating every voter equally and preserving aggregate welfare. One possible solution is storable votes: granting each voter a budget of votes to cast as desired over multiple decisions. During the 2006 student elections at Columbia University, we tested a simple version of this idea: voters were asked to rank the importance of the different contests and to choose where to cast a single extra "bonus vote," had one been available. We used these responses to construct distributions of intensities and electoral outcomes, both without and with the bonus vote. Bootstrapping techniques provided estimates of the probable impact of the bonus vote. The bonus vote performs well: when minority preferences are particularly intense, the minority wins at least one of the contests with 15--30 percent probability; and, when the minority wins, aggregate welfare increases with 85--95 percent probability. When majority and minority preferences are equally intense, the effect of the bonus vote is smaller and more variable but on balance still positive.

"Storable Votes: Giving Voice to Minorities without Sacrificing Efficiency "
with Thomas Palfrey and Raymond Riezman

CESIfo DICE Report 2007, 3.

"Minorities and Storable Votes"
with Thomas Palfrey and Raymond Riezman

The paper studies a simple voting system that has the potential to increase the power of minorities in committees without sacrificing aggregate efficiency. Storable votes grant each voter a stock of votes to spend as desired over a series of sequential binary decisions. By accumulating votes on issues that it deems most important, the minority can win occasionally. But because the majority typically can outvote it, the minority wins only if its strength of preference is high and the majority's strength of preference is low. The result is that aggregate efficiency either falls little or in fact rises. The theoretical predictions of our model are confirmed by a series of experiments: the frequency of minority victories, the relative payoff of the minority versus the majority, and the aggregate payoffs all match the theory.

"A Simple Scheme to Improve the Efficiency of Referenda "
with Andrew Gelman

This paper proposes a simple scheme designed to elicit and reward intensity of preferences in referenda: voters faced with a number of contemporaneous binary proposals are given one regular vote for each proposal plus an additional number of bonus votes to cast as desired. Decisions are taken according to the majority of votes cast. In our base case, where there is no systematic difference between proposals' supporters and opponents, there is always a positive number of bonus votes such that ex ante utility is increased by the scheme, relative to simple majority voting. When the distributions of valuations of supporters and opponents differ, the improvement in efficiency is guaranteed if the distributions can be ranked according to first order stochastic dominance. If they are, however, the existence of welfare gains is independent of the exact number of bonus votes.

"Information Channels in Labor Markets. On the Resilience of Referral Hiring "
with Nobuyuki Hanaki

Economists and sociologists disagree over markets' potential to assume functions typically performed by networks of personal connections, first among them the transmission of information. This paper begins from a model of labor markets where social ties are stronger between similar individuals and firms employing productive workers prefer to rely on personal referrals than to hire on the anonymous market (Montgomery (1991)). However, we allow workers in the market to engage in a costly action that can signal their high productivity, and ask whether the possibility of signaling reduces the reliance on the network. We find that the network is remarkably resilient. To be effective, signaling must fulfill two contradictory requirements: unless the signal is extremely precise, it must be expensive or it is not informative; but it must be cheap, or the network can undercut it.

"An Experimental Study of Storable Votes"
with Andrew Gelman and Thomas Palfrey
The storable votes mechanism is a method of voting for committees that meet periodically to consider a series of binary decisions. Each member is allocated a fixed budget of votes to be cast as desired over the multiple decisions. Voters are induced to spend more votes on those decisions that matter to them most, shifting the ex ante probability of winning away from decisions they value less and towards decisions they value more, typically generating welfare gains over standard majority voting with non-storable votes. The equilibrium strategies have a very intuitive feature–the number of votes cast must be monotonic in the voter’s intensity of preferences–but are otherwise diffcult to calculate, raising questions of practical implementation. In our experiments, realized effciency levels were remarkably close to theoretical equilibrium predictions, while subjects adopted monotonic but off-equilibrium strategies. We are lead to conclude that concerns about the complexity of the game may have limited practical relevance.

"Storable Votes"
 Motivated by the need for more flexible decision-making mechanisms in the European Union, the paper proposes a simple but novel voting scheme for binary decisions taken by committees that meet regularly over time. At each meeting, committee members are allowed to store their vote for future use; the decision is then taken according to the majority of votes cast. The possibility of shifting votes intertemporally allows agents to concentrate their votes when preferences are more intense, and although the scheme will not in general achieve full efficiency, making votes storable typically leads to ex ante welfare gains. The result appears clearly and can be proven rigorously in the case of 2 voters. With more voters, the analysis suggests that the welfare improvement should continue to hold if one of the following conditions is satisfied: (i) the number of voters is above a minimum threshold; (ii) preferences are not too polarized; (iii) the horizon is long enough. 

"Games for Central Bankers: Markets v/s politics in public policy decisions."
This paper questions the link between the establishment of a common currency among several countries and the necessity of political coordination. It begins by discussing why conducting a single monetary policy is thought to be easier within a single political unit. It then proceeds to enquire whether market mechanisms could be used to choose optimally the common policy of heterogenous actors, and thus provide an alternative to political decision-making. The advantage of market mechanisms is that they are transparent, predictable, and usually more efficient. In particular, the paper studies a simple game through which national representatives could choose the monetary policy of a single, multinational central bank. There are no fundamental logical objections or impossible practical obstacles to such market games, and even if they are rejected on principle they are useful in suggesting desirable amendments to traditional voting schemes.

"The Role of Market Size in the Formation of Jurisdictions."
Administrative and political reorganization is being actively debated even in the mature, stable economies of Western Europe. This paper investigates the possibility that such a reorganization is tied to the integration of economic markets. The paper describes a model where heterogeneous individuals form coalitions for the provision of a public good and shows that the number and composition of these jurisdictions depend on the overall size of the market. The range of economic activities engaged in by jurisdiction members increases when the size of the market increases, and so does the range of their preferences over the public good. The result is a change in the endogenous borders of the jurisdictions, and a reorganization of all coalitions. The optimal number of jurisdictions is unique and increases with market size. In the absence of compensating transfers, however, the decentralized equilibrium need not be optimal and is not unique, although there is no restriction on individuals’ ability to coordinate the formation of coalitions. It remains true that a large enough increase in market size will trigger an increase in the number of jurisdictions.

"Tradable Deficit Permits:"
"Efficient Implementation of the Stability Pact in the European Monetary Union."
Borrowing from the experience of environmental markets, this paper proposes a system of tradable deficit permits as an efficient mechanism for implementing fiscal constraints in the European Monetary Union: having chosen an aggregate target for the Union and an initial distribution of permits, EMU countries could be allowed to trade rights to deficit creation. The scheme exploits countries’ incentives to minimize their costs, is transparent, flexible in accommodating idiosyncratic shocks and allows for adjustments in case of Europe-wide recessions. In addition, it need not treat all countries identically and can be designed to penalize countries with higher debt to GDP ratios. Finally, the scheme rewards countries for reducing their deficit below the initial allowance, lending credibility to the Stability Pact’s goal of a balanced budget in the medium run. 

"Anonymous Market and Group Ties in International Trade."
with James E. Rauch
When trade involves differentiated products, preferential ties to a group settled abroad facilitate an exporter's entry into the foreign market by providing information and access to distribution channels. This contrasts with the difficulties experienced by an unattached producer unfamiliar with the foreign environment. We build a simple general equilibrium model of trade that formalizes this observation. Output is generated through bilateral matching of agents spanning a spectrum of types. In the domestic market every trader knows the type of all others and can approach whomever he chooses; when matching abroad, instead, traders lack the information necessary to choose their partner's type. A minority of individuals has access to group ties that extend complete information to international matches. The existence of informational barriers reduces the volume of trade, and thus by increasing total trade group ties are beneficial to the economy as a whole. However, the ties have significant distributional effects because they modify the composition of the market. Only the more desirable types choose to match through the group, worsening the prospects of successful international partnerships for everybody else. The volume of trade and expected per capita income rise for group members, but fall for non-members. Whether or not they have access to the ties, individuals with the weakest domestic alternatives are always hurt.

"Public Goods in Trade on the Formation of Markets and Jurisdictions."
with Jonathan S. Feinstein
Must the integration of markets be accompanied by the harmonization of societies' institutions? To address this question we construct a model of heterogenous traders where the return from private exchange is directly affected by the public good individuals have access to. Trade takes place in the market, whereas the public good is chosen and financed by the jurisdiction, and each individual chooses which market and which jurisdiction to join among the many that form in equilibrium. Although trade between members of different jurisdictions entails transaction costs, we find that market integration is neither necessary nor sufficient for the integration of jurisdictions: only at intermediate market sizes must trading partners belong to a single jurisdiction. When markets are small multiple jurisdictions can exist, although a single one would be preferable; when markets are large multiple jurisdictions are both possible and desirable.

"Overcoming Informational Barriers to International Resource Allocation:"
"Price and Group Ties."
with James E. Rauch
Incomplete information in the international market creates difficulty in matching agents with productive opportunities and interferes with the ability of prices to allocate scarce resources across countries. Resource-price differentials may not be eliminated and domestic resource supplies may have excessive influence on domestic resource prices. Information-sharing networks among internationally dispersed ethnic minorities or business groups can improve the allocation of resources, though at the same time they may hurt those excluded from the preferential information channels. However, when ties are denser between countries with small resource price differences than between countries with large resource price differences, such networks can worsen the allocation of resources and reduce the value of world output.