SEQUENTIAL OR SIMULTANEOUS ELECTIONS? A WELFARE ANALYSIS

• Published date: 01 August 2015
• Author: Brian Knight,Patrick Hummel
• DOI: http://doi.org/10.1111/iere.12124
• Date: 01 August 2015

INTERNATIONAL ECONOMIC REVIEW

Vol. 56, No. 3, August 2015

SEQUENTIAL OR SIMULTANEOUS ELECTIONS? A WELFARE ANALYSIS∗

BYPATRICK HUMMEL AND BRIAN KNIGHT1

Google Inc., U.S.A.; Brown University, U.S.A.

Should all voters vote on the same day or should elections be staggered? Using a model of voting and social learning,

we illustrate that sequential elections place too much weight on early states but also provide late voters with valuable

information. Simultaneous elections equally weigh states but place too much weight on voter priors, providing an

inappropriate advantage to front-runners. Simultaneous elections are thus preferred if the front-runner advantage is

small, but sequential elections are preferred if the advantage is large. Our quantitative welfare analysis of presidential

primaries suggests that simultaneous systems slightly outperform sequential systems.

“ . .. for years concerns have been raised regarding the calendar that some believe gives a dispropor-

tionate influence to these two early states.”

— David Price, Commission on Presidential Nomination Timing and Scheduling, October 1, 2005

“We need to preserve the possibility for lesser known, lesser funded candidates to compete, and a

national primary on February 5th will not do that.”

— Terry Shumaker, Commission on Presidential Nomination Timing and Scheduling, December 5,

2005

1. INTRODUCTION

Although voting occurs simultaneously in many electoral and legislative settings, there are

also settings in which voting occurs sequentially. Under a roll call ballot, for example, votes

are recorded one-by-one with participants observing the votes of those preceding them before

casting their own ballots. In the electoral context, presidential general elections were held on

different days in different states prior to 1872. A related issue involves the release of voting

returns on election day, especially in countries with multiple time zones.

This distinction between simultaneous and sequential systems is particularly salient in the

design of presidential primary systems, which have traditionally followed a calendar in which

Iowa and New Hampshire vote first, followed by a group of states on the first Tuesday in

February and another group on the first Tuesday in March. This is followed by several months

of further elections, with the process often continuing into early summer.

Given concerns associated with the current system, several alternatives have been proposed.

At the extreme, advocates of a true national primary, in which every state would vote on the

same date, point toward a more efficient and fair system. Hybrid systems, which move toward

a simultaneous system but retain some features of the current sequential system, include the

rotating regional primary system, under which Iowa and New Hampshire would vote first,

followed by four weekly rounds of regional primaries, with the order of the regions rotating

from election to election.

∗Manuscript received July 2013; revised January 2014.

1We thank Nageeb Ali, Gerard Padro i Miquel, conference participants at the Princeton Conference on Political

Economy, the Center for the Study of American Politics Summer Conference, and the NBER Summer Institute, and

seminar participants at the University of Pennsylvania, the University of Miami, Miami University, the University

of Michigan, and the New Economic School. Please address correspondence to: Brian Knight, 64 Waterman Street,

Providence, RI 02912. E-mail: Brian Knight@brown.edu.

851

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(2015) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

852 HUMMEL AND KNIGHT

Debates over the choice between traditional sequential calendars and these alternative, more

compressed calendars typically focus on trading off the relative advantages of the two systems.

In particular, opponents of sequential systems argue that early states have disproportionate

influence, whereas supporters argue that it enhances competition since dark horse candidates

can better emerge from the field of candidates. Under simultaneous elections, by contrast, states

would have equal influence but dark horse candidates may not be provided with sufficient

opportunity to compete. Although these factors have dominated the debate, there has been

little formal analysis of this trade-off, and there have also been no attempts to weigh the relative

importance of these advantages and disadvantages of the two systems.

In this article, we use the positive model of voting and social learning developed in Knight

and Schiff (2010) in order to conduct a normative analysis of this trade-off. In the model, vot-

ers are uncertain over candidate quality but have some private information. Under sequential

elections, voters in late states attempt to infer the information of voters in early states from

voting returns. Using this model, we compare both simultaneous and sequential elections to a

public information benchmark, under which all voters observe all relevant signals. We show

theoretically that neither system is optimal and that there is indeed a trade-off between vot-

ers equally weighing preferences and information under simultaneous systems and late voters

being better informed under sequential elections. We then develop welfare expressions based

upon aggregate voter utility and show that simultaneous elections tend to dominate when the

advantage of the front-runner is small. When this advantage is large, by contrast, sequential

election systems tend to dominate as they provide greater opportunities for dark horse candi-

dates of unexpectedly high quality to emerge from the field. Finally, we conduct an empirical

welfare analysis based upon data from presidential primaries, and the estimates suggest that

simultaneous election systems outperform sequential election systems.

The article proceeds as follows: We first discuss the related literature and then review the pos-

itive theoretical model of voting and social learning. Using this model, we provide a comparison

of sequential and simultaneous systems and show that either system might be preferred from

a welfare perspective. Finally, we conduct a numerical welfare analysis that examines a variety

of electoral institutions, with a focus on comparing sequential and simultaneous systems.

2. LITERATURE REVIEW

This article is at the intersection of four literatures: social learning, theoretical analyses of

sequential voting systems, empirical analyses of sequential voting systems in the context of

presidential primaries, and optimal electoral institutions. We discuss each, in turn, below.

2.1. Social Learning. The literature on social learning began with Welch (1992), Bikhchan-

dani et al. (1992), and Banerjee (1992). In these models, agents take actions in a predetermined

sequence, individual payoffs depend only upon individual actions, and late movers have an

opportunity to observe the actions of early movers. If actions are discrete and payoffs are suffi-

ciently correlated, a herd may form in which agents ignore their private information and simply

follow the actions of those earlier in the sequence. Note that despite the fact that information

may be lost in this process, simultaneous choice never dominates a sequential order from a wel-

fare perspective. This follows from the fact that individual payoffs depend only upon individual

actions, and thus agents moving in a sequence that would rationally ignore the behavior of early

agents were doing so in their best interests. In the voting context, by contrast, individual payoffs

depend upon the actions of all agents. Thus, if it is optimal to do so, agents will rationally ignore

the behavior of early agents.

2.2. Theoretical Analyses of Sequential Voting. Several papers have examined this issue of

social learning in the electoral context with a focus on binary elections. In a model with two

candidates and strategic voters, Dekel and Piccione (2000) show that every equilibrium of

the simultaneous game is an equilibrium of the sequential game. This follows from the fact

SEQUENTIAL OR SIMULTANEOUS? 853

that voters condition on being pivotal and hence behave as if exactly half of the other voters

favor one option over the other. Thus, the identity of the early voters is irrelevant, and voters

do not condition on the behavior of those earlier in the sequence. The converse that every

equilibrium of the sequential game is an equilibrium of the simultaneous game, however, is

not necessarily true. In particular, Ali and Kartik (2012) construct equilibria in which late

voters do condition on the behavior of early voters. Other theoretical analyses of sequential

elections include Battaglini (2005), who focuses on voter turnout, Hummel (2012), who focuses

on multicandidate elections, Morton and Williams (1999, 2001), who focus on learning about

candidate ideology from early voters and conduct corresponding experimental tests, Hummel

(2011), who addresses the desire to avoid a long and costly primary, Aldrich (1980) and Klumpp

and Polborn (2006), who examine campaign finance in the context of sequential elections, and

Strumpf (2002), who examines candidate incentives for exiting the election.

Two other theoretical papers have investigated the issue of competition when comparing

simultaneous and sequential elections. In Selman (2010), there are two candidates, one of

which is high quality and one of which is low quality, and voters receive private information

about which candidate is of high quality. Loyal voters always vote for their preferred candidate,

whereas uncommitted voters support the candidate of higher expected quality. Unlike our

model, neither candidate is favored in terms of voter priors over quality. In the context of his

model, Selman shows that the sequential system is preferred when loyal voters are imbalanced

and the quality of information is low. Although competition also plays a role in our comparison

between sequential and simultaneous elections, the mechanism is quite different. Unlike Selman

(2010), candidates in our model are advantaged due to voter priors, and the advantage of the

sequential system is that voters place less weight on these priors.

A second paper, Callandar (2007), compares sequential and simultaneous elections in the

context of a model in which voters are strategic, in the sense of conditioning their vote on

being pivotal, and also prefer to vote for winners. There are two candidates, one of which

is high quality and one of which is low quality, and voters receive private information about

which candidate is of high quality. In the context of this model, Callander shows that sequential

elections outperform simultaneous elections when voter priors significantly favor one of the two

candidates. Although this result is similar to our result regarding competition, the underlying

mechanism is quite different. In particular, if voter priors significantly favor one of the two

candidates, then under simultaneous voting, voters have an incentive to simply ignore their

private information and vote for the candidate that is more likely to win based on their priors.

However, when the preference for voting for the winner disappears, sequential and simultaneous

are both efficient. Our comparison between the two systems, by contrast, is not based upon a

preference for voting for the winner.

An additional contribution of our article relative to both Selman (2010) and Callander (2007)

is our empirical analysis. In particular, our article represents the first attempt to quantify the

trade-off between competition and equal weighting of information.

2.3. Empirical Analyses of Sequential Voting. Empirical analyses of presidential primary

systems include Knight and Schiff (2010), who, using daily polling data from the 2004 presidential

primary, document momentum effects and provide empirical support for a social learning

interpretation. Note that the paper, Knight and Schiff (2010), is purely positive in nature and

does not address the normative question of which system is welfare-preferred. Bartels (1987,

1988) examines polling data in 1984 and shows that candidate viability plays a key role in

momentum effects. Bartels (1985) and Kenney and Rice (1994) also examine other possible

empirical motivations for momentum effects using data from the 1980 and 1988 presidential

primaries. Finally, there is a series of papers, including Adkins and Dowdle (2001), Steger

et al. (2004), and Steger (2008), documenting that early states have a disproportionate influence

in terms of selecting the winning candidate in presidential primaries. These papers are all

relevant in the sense that they document important differences in electoral outcomes between

simultaneous and sequential systems.