Abstract
Sequential multi-battle contests are predicted to induce lower expenditure than simultaneous contests. This prediction is a result of a “New Hampshire Effect”—a strategic advantage created by the winner of the first battle. Although our laboratory study provides evidence for the New Hampshire Effect, we find that sequential contests generate significantly higher (not lower) expenditure than simultaneous contests. This is mainly because in sequential contests, there is significant over-expenditure in all battles. We suggest sunk cost fallacy and utility of winning as two complementary explanations for this behavior and provide supporting evidence.
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Notes
Just as candidates who do poorly in the New Hampshire primary frequently drop out, the lesser-known, underfunded candidates who do well in the primary suddenly become serious contenders to win the party nomination, garnering tremendous momentum both in terms of media coverage and campaign funding. In 1992, Bill Clinton, a little known governor of Arkansas did surprising well, and was labeled the “Comeback Kid” by the national media. In 2000, John McCain emerged as George Bush’s principal challenger only after an upset victory in New Hampshire, and a similar comeback was made by John Kerry in the 2004 primary.
In a multi-candidate race, even a second-place finish in New Hampshire primary increases a candidate’s final vote by 17.2% (Mayer 2004).
The total economic impact of 2000 primary on New Hampshire’s economy was estimated to be $264 million. The state also receives a diverse array of ‘special policy concessions’ as a result of its privileged position in the presidential nomination process (Busch and Mayer 2004). Originally held in March, the date of the New Hampshire primary has been moved up repeatedly to maintain its status as first (a tradition since 1920). In fact, the state law requires that its primary must be the first in the nation.
Our experiment compares two extreme benchmarks: a completely sequential contest to a completely simultaneous contest. Present day primary system, however, has a mixed temporal structure. The nomination process starts with a series of sequential elections held in various states (Iowa caucus, New Hampshire primary, etc.) followed by days such as “Super Tuesday.” Klumpp and Polborn (2006) state that the results of a completely sequential contest can apply to a mixed temporal contest, as long as the latter begins with at least a few sequential battles.
The contest model is complementary to the voters’ participation model (Morton and Williams 1999; Battaglini et al. 2007). In the voters’ participation model the probability of winning an electoral district by a candidate depends on the number of votes received, while in the contest model such a probability depends on the relative campaign expenditure by each candidate in that district. The complementarity between the two models arises because one of the reasons for the New Hampshire Effect that is commonly discussed in political science is information aggregation, which is implicit in voting models. For instance, Morton and Williams (1999) compare sequential and simultaneous voting and find that in sequential voting later voters use early outcomes to infer information about asymmetric candidates, and thus make better informed choices that reflect their true preferences. Battaglini et al. (2007) find that sequential voting aggregates information better than simultaneous voting and is more efficient in some information environments, but sequential voting is inequitable because early voters bear more participation costs. By assuming that both candidates are symmetric and by abstracting from costly voter participation decision, we are able to isolate how candidates’ relative expenditure alone determines the likelihood of winning current and future electoral districts. That is, we examine the New Hampshire Effect resulting solely from candidates’ campaign expenditure decisions.
One could also argue that the original formulation of a Colonel Blotto game by Borel (1921) is a starting point of the multi-battle contest literature.
Building on these models, subsequent papers investigated the ramification of various factors such as the sequence ordering of decisions, number of battles, asymmetry between players, effect of carryover, effect of uncertainty, the impact of discount factor and intermediate prizes (Harris and Vickers 1985, 1987; Leininger 1991; Baik and Lee 2000; Szentes and Rosenthal 2003; Roberson 2006; Kvasov 2007; Konrad and Kovenock 2009).
The solution to this game can be found in Friedman (1958).
In the sequential contest, the total expected expenditure by both players in battle 1 is 32.8; in battle 2 is 18.8; and since battle 3 is likely to occur with probability 0.25, the unconditional expected expenditure in battle 3 is 25.
48% of our subjects identified as males and 52% as females. The average age of the participants was 19.63 and ranged between 18 and 28. More than 60% of the subjects were sophomores or freshmen and about 70% were majoring in business and economics.
Subjects also made 15 choices in simple lotteries, similar to Holt and Laury (2002), at the beginning of the experiment. These were used to elicit their risk aversion preferences, and subjects were paid for one randomly selected choice. We did not find any interesting patterns or correlations between risk attitudes and behavior in contests. So, we omit any discussion from the article.
100 francs is substantially higher than the highest possible equilibrium bid, but we decided not to constrain individual bidding to be consistent with the theoretical model which assumes no budget constraints. Additionally, we wanted to avoid potential unintended behavioral consequences since enforcing even non-binding budget constraints can unexpectedly affect subjects’ behavior (Price and Sheremeta 2011; Sheremeta 2011).
We chose to select only 2 periods for payment in order to avoid intra-experimental income effects (McKee 1989). In addition, subjects were paid for their lottery choice from the risk elicitation procedure.
We have checked the robustness of these results by estimating a mixed-effects panel model for each treatment (see Table B1 in Appendix B). We have 1440 observations for each treatment (6 sessions × 12 subjects × 20 periods). The dependent variable in the regression is the total expenditure and the independent variables are a constant and a period trend. The model included a mixed-effects error structure with a 3-way nested model (observations nested within a session and then within a subject) to account for the multiple decisions made by each subject and random re-matching within a session. A standard Wald test, conducted on estimates of regression models, shows that expenditure in the sequential contest is significantly higher than predicted (p value < 0.01) and for the simultaneous contest it is not different from the prediction (p value = 0.60). Hypothesis testing with a few clusters (sessions) can result in over-rejection of the null hypothesis. To address this concern, we also conducted regressions based on Cameron et al. (2008) wild cluster approach. The results remain the same—expenditure in the sequential contest is significantly higher than predicted and for the simultaneous contest it is not different from the prediction.
See Table B1 in Appendix B.
Mixed-effects panel regressions collaborate the results of the non-parametric statistical tests (see Table B2 in Appendix B). In estimating these regressions, we used total expenditure as the dependent variable and a treatment dummy-variable, a period trend, and a constant as the independent variables. Regressions based on Cameron et al. (2008) wild cluster approach produce similar results.
A mixed-effects panel regression collaborates the results of the non-parametric statistical tests (see Table B3 in Appendix B). In estimating this regression, we used a battle 2 expenditure as the dependent variable and a dummy-variable for winning battle 1, a period trend, and a constant as the independent variables. A regression based on Cameron et al. (2008) wild cluster approach produces similar results.
The non-parametric statistical tests are also corroborated by mixed-effect panel regressions (see Table B4 in Appendix B). Regressions based on Cameron et al. (2008) wild cluster approach produce similar results.
See Table B4 in Appendix B.
Explanations for over-expenditure in single-battle contests include non-monetary utility of winning (Sheremeta 2010a, b; Cason et al. 2012, 2017, 2018), mistakes (Sheremeta 2011), misperception of probabilities (Shupp et al. 2013; Chowdhury et al. 2014), evolutionary bias (Mago et al. 2016), and impulsivity (Sheremeta 2016).
This conclusion comes from estimating a mixed-effect panel regression.
The non-parametric statistical tests are also collaborated by mixed-effect panel regressions (see Table B5 in Appendix B). In estimating these regressions, we used a battle 2 expenditure as the dependent variable and a treatment dummy-variable, a period trend, and a constant as the independent variables. Regressions based on Cameron et al. (2008) wild cluster approach produce similar results.
See Table B5 in Appendix B.
As evidenced in the prior discussion, sunk cost fallacy cannot explain all the deviations from the theory. Even in the modified sessions, expenditure in battle 2 remains significantly higher relative to the theoretical predictions for both winner and loser of battle 1. Also, the sunk cost fallacy cannot explain the fact that battle 1 loser (who presumably spent less resources in battle 1, and should not be subject to sunk cost fallacy as much as battle 1 winner) does not give up in battle 2.
That is, there is no allocation bias such as that observed in Colonel Blotto games (Chowdhury et al. 2013), where players who read and write from left to right horizontally in their native language tend to allocate greater expenditure to the battles on the left.
It is important to emphasize, however, that the “guerilla warfare” strategy is not an equilibrium strategy. In fact, in the context of a lottery contest success function, the only equilibrium is to allocate resources uniformly across all battles (Klumpp and Polborn 2006; Kovenock et al. 2010; Kovenock and Roberson 2012).
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Acknowledgements
We thank David Cooper, the Editor of this journal, and two anonymous referees for their valuable suggestions. We have benefitted from the helpful comments of Tim Cason, Sera Linardi, Vai-Lam Mui, Andrew Healy, James Konow, Rebecca Morton, Tim Shields, Stergios Skaperdas, Jonathan Wight, seminar participants at Loyola Marymount University, University of California Irvine, University of Richmond and participants at the International Economic Science Association Conference in Copenhagen, the Virginia Association for Economists Meeting, and the Pittsburgh Behavioral Models of Politics Conference for helpful comments. University of Richmond provided funds for conducting the experiments. The usual disclaimers apply.
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Mago, S.D., Sheremeta, R.M. New Hampshire Effect: behavior in sequential and simultaneous multi-battle contests. Exp Econ 22, 325–349 (2019). https://doi.org/10.1007/s10683-018-9569-0
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DOI: https://doi.org/10.1007/s10683-018-9569-0