The Size of Countries: Does it Matter?

Borders are a man made institution, and as such their shape cannot be taken as part of the physical landscape. The size of countries is endogenous to politico economic forces. This paper discusses recent efforts by economists to study three related question: what determines the evolution of the size of countries? Does size matter for economic success? Given the trend toward decentralization and of creation of supernational unions like the EU, is the meaning of national borders evolving?

Board structures around the world: An experimental investigation

We model and experimentally examine the board structure-performance relationship. We examine single-tiered boards, two-tiered boards, insider-controlled boards, and outsider-controlled boards. We find that even insider-controlled boards frequently adopt institutionally preferred rather than self-interested policies. Two-tiered boards adopt institutionally preferred policies more frequently, but tend to destroy value by being too conservative, frequently rejecting good projects. Outsidercontrolled single-tiered boards, both when they have multiple insiders and only a single insider, adopt institutionally preferred policies most frequently. In those board designs where the efficient Nash equilibrium produces strictly higher payoffs to all agents than the coalition-proof equilibria, agents tend to select the efficient Nash equilibria.

Constitutional Design and Political Communication

This paper models the constitutional design process, and points out the importance of political communication (defined as the level of information about the social distribution of policy preferences that individuals hold, at the time of this process) on the "extent" of "democratic restraints" of the socially preferred constitution and on the welfare derived by the society from its implementation. The results demonstrate that the level of political communication has a positive effect on the level of democracy of the socially preferred constitution and on social welfare. Moreover, it is proved that, even if there exist no tolerance for dictatorship by societies in general, the level of democracy demanded by the society, reaches the maximum possible level, only if political communication is "perfect". That is, the socially preferred constitution in cases of "imperfect" political communication incorporates both dictatorial and democratic elements.constitution, political communication, democracy

On the Distortion of Voting with Multiple Representative Candidates

We study positional voting rules when candidates and voters are embedded in a common metric space, and cardinal preferences are naturally given by distances in the metric space. In a positional voting rule, each candidate receives a score from each ballot based on the ballot's rank order; the candidate with the highest total score wins the election. The cost of a candidate is his sum of distances to all voters, and the distortion of an election is the ratio between the cost of the elected candidate and the cost of the optimum candidate. We consider the case when candidates are representative of the population, in the sense that they are drawn i.i.d. from the population of the voters, and analyze the expected distortion of positional voting rules. Our main result is a clean and tight characterization of positional voting rules that have constant expected distortion (independent of the number of candidates and the metric space). Our characterization result immediately implies constant expected distortion for Borda Count and elections in which each voter approves a constant fraction of all candidates. On the other hand, we obtain super-constant expected distortion for Plurality, Veto, and approving a constant number of candidates. These results contrast with previous results on voting with metric preferences: When the candidates are chosen adversarially, all of the preceding voting rules have distortion linear in the number of candidates or voters. Thus, the model of representative candidates allows us to distinguish voting rules which seem equally bad in the worst case

Communication, Distortion, and Randomness in Metric Voting

In distortion-based analysis of social choice rules over metric spaces, one assumes that all voters and candidates are jointly embedded in a common metric space. Voters rank candidates by non-decreasing distance. The mechanism, receiving only this ordinal (comparison) information, should select a candidate approximately minimizing the sum of distances from all voters. It is known that while the Copeland rule and related rules guarantee distortion at most 5, many other standard voting rules, such as Plurality, Veto, or $k$-approval, have distortion growing unboundedly in the number $n$ of candidates. Plurality, Veto, or $k$-approval with small $k$ require less communication from the voters than all deterministic social choice rules known to achieve constant distortion. This motivates our study of the tradeoff between the distortion and the amount of communication in deterministic social choice rules. We show that any one-round deterministic voting mechanism in which each voter communicates only the candidates she ranks in a given set of $k$ positions must have distortion at least $\frac{2n-k}{k}$; we give a mechanism achieving an upper bound of $O(n/k)$, which matches the lower bound up to a constant. For more general communication-bounded voting mechanisms, in which each voter communicates $b$ bits of information about her ranking, we show a slightly weaker lower bound of $\Omega(n/b)$ on the distortion. For randomized mechanisms, it is known that Random Dictatorship achieves expected distortion strictly smaller than 3, almost matching a lower bound of $3-\frac{2}{n}$ for any randomized mechanism that only receives each voter's top choice. We close this gap, by giving a simple randomized social choice rule which only uses each voter's first choice, and achieves expected distortion $3-\frac{2}{n}$.Comment: An abbreviated version appear in Proceedings of AAAI 202

Comparing Election Methods Where Each Voter Ranks Only Few Candidates

Election rules are formal processes that aggregate voters preferences, typically to select a single candidate, called the winner. Most of the election rules studied in the literature require the voters to rank the candidates from the most to the least preferred one. This method of eliciting preferences is impractical when the number of candidates to be ranked is large. We ask how well certain election rules (focusing on positional scoring rules and the Minimax rule) can be approximated from partial preferences collected through one of the following procedures: (i) randomized-we ask each voter to rank a random subset of $\ell$ candidates, and (ii) deterministic-we ask each voter to provide a ranking of her $\ell$ most preferred candidates (the $\ell$-truncated ballot). We establish theoretical bounds on the approximation ratios and we complement our theoretical analysis with computer simulations. We find that mostly (apart from the cases when the preferences have no or very little structure) it is better to use the randomized approach. While we obtain fairly good approximation guarantees for the Borda rule already for $\ell = 2$, for approximating the Minimax rule one needs to ask each voter to compare a larger set of candidates in order to obtain good guarantees

The Dynamic Reform of Political Institutions

This paper introduces a class of games designed to study dynamic, endogenous reform of political institutions. Dynamic political games (DPGs) are dynamic games in which institutional choice is both recursive and instrumental. Future political aggregation rules are decided under current ones, and institutional choices do not affect payoffs or technology directly. We examine properties of the Markovian equilibria of DPGs. In any equilibrium, institutional reform occurs if the subsequent political rule is chosen to be different than the present one. Which environments exhibit institutional reform and which tend toward institutional stability? Private (public) sector decisions are said to be inessential if, roughly, they can always be replaced by decisions in the public (private) sector in a social planner's payoff. We show that if the private sector is inessential, then institutional reform never occurs. However, if public sector decisions are inessential, then institutional reform must occur. The result suggests that an ineffective private sector is conducive to institutional stability, while an ineffective public sector is conducive to change. We also address the ``political fixed point problem" that arises in a model of recursive institutional choice. Namely, the current political rule (e.g., majority voting) admits a solution only if all feasible political rules admit solutions in all future dates. If the class of political rules is dynamically consistent then DPGs are shown to admit political fixed points. This result is used to prove two equilibrium existence theorems, one of which implies that all decision rules are smooth functions of the economic stateRecursive, dynamic political games, institutional reform, political fixed points, inessential.