Bullet voting

Bullet voting[1] (also single-shot voting[2] and plump voting[3]) is a voting tactic, usually in multiple-winner elections, where a voter is entitled to vote for more than one candidate, but instead votes for only one candidate.

A voter might do this either because it is easier than evaluating all the candidates, or as a form of tactical voting. This tactic can be used to maximize the chance that the voter's favourite candidate will be elected, while increasing the risk that other favoured candidates will lose. A group of voters using this tactic consistently has a better chance for one favourite candidate to be elected.[4][5]

Election systems that satisfy the later-no-harm criterion discourage any value in bullet voting. These systems either do not ask for lower preferences (like plurality) or promising to ignore lower preferences unless all higher preferences are eliminated.

Some elections have tried to disallow bullet voting, and require the casting of multiple votes, because it can empower minority voters. Minority groups can defeat this requirement if they are allowed to run as many candidates as seats being elected.[6][7]

Single winner elections

Plurality voting only allows a single vote, so bullet voting is effectively mandatory. Voting for more than one candidate is called an overvote and will invalidate the ballot.

In contrast, approval voting allows voters to support as many candidates as they like, and bullet voting can be a strategy of a minority, just as in multiple winner elections (see below). Such voting would be for their sincere favourite, so would not result in the same pathologies seen in Plurality voting where voters are encouraged to bullet vote for a candidate who is not their favourite. Bucklin voting[8] and Borda voting used ranked ballots and both allow the possibility that a second choice could help defeat a first choice, so bullet voting might be used to prevent this.

Instant-runoff voting and contingent vote allow full preferences to be expressed and lower preferences have no effect unless the higher ones have all been eliminated. Therefore bullet voting has no tactical advantage in these cases: on the contrary, it can lead to loss of influence, if no ranking is expressed among the final two candidates.

Examples on ranked ballots
Bullet vote Preference vote
Marked a single preference Marked all preferences the same
(Lower rankings for the same candidate are ignored)		 In process marking third preference

Multiple winner elections
N seat elections
SystemVotes
Approval voting
Range voting
Borda voting		Point
scores
Plurality-at-large votingN
Limited voting
 		N-1
N-2
...
Single nontransferable vote
(Whole vote)		1
Instant runoff voting
(Whole vote)		1
Cumulative voting
(Explicit divided vote)		1
Single transferable vote
(Implicit divided vote)		1

Multiple votes are often allowed in elections with more than one winner. Bullet voting can help a first choice be elected, depending on the system:

  • Plurality-at-large voting (Bloc-voting) allows up to N votes for elections with N winner elections. In this system, a voter who prefers a single candidate and is concerned his candidate will lose has a strong incentive to bullet vote to avoid a second choice helping to eliminate a first choice.[9] Even so, a united majority of voters in plurality-at-large can control all the winners despite any strategic bullet voting by a united minority.
  • Approval voting used in a multi-winner election works the same way as Plurality-at-large, but allows more votes than winners. This results in a body that is less representative than a body elected under a proportional voting method, but would still have the same ideological center as the population[10]. 100% bullet voting under Approval Voting in a multi-winner election is unlikely, as voters are incentivized to vote for acceptable moderates in addition to their favourite candidates to avoid being locked out of the election entirely.[11]
    • Range voting is a generalization of Approval voting where gradations of support can be given for each candidate. Here bullet voting would refer to giving 100% support for one candidate and 0% for all other candidates, just like Approval bullet voting.
    • Borda voting assign multiple votes based on ranked ballots, like 3 votes for first, 2 votes for second, and 1 vote for third choice. This encourages minority voters to bullet vote (not using all the rankings). If voters are requires to rank all the candidates, it further encourages voters to (insincerely) bury strongest rivals at the lowest rankings.
  • Limited voting goes the opposite way as Approval, allowing fewer votes than winners. This reduces the ability of a united majority of voters to pick all the winners, and gives more influence to minority voters who would bullet vote anyway.[12]
    • A single nontransferable vote limits everyone to one vote, effectively making bullet voting mandatory, minimizing the power of a majority of voters to pick all the winners, and can work well if there are only a few more candidates as winners.[13]
Bullet voting in Cumulative voting allows multiple votes for one candidate.
  • Cumulative voting allow up to N votes for N winner elections which can be distributed between multiple candidates or all given to one candidate. Effectively, this is one vote which can be fractionally divided among more than one candidate. This removes any penalty to bullet voters, who support a single candidate, and it enables the possibility of a united minority to elect at least one winner despite a united majority voting for all other candidates.
  • Instant runoff voting and Single transferable vote take away the incentive for bullet voting (leaving candidates unranked) entirely since lower rankings are only used if all higher choices are elected or eliminated. STV goes one step further than IRV, computing a threshold for electability, like 20% for 4 candidates, and when a candidate is elected, supporters get a surplus fraction of their vote transferred to their next choice. This increases the value of giving full preferences.

Burr Dilemma

The Burr Dilemma exists in an election of multiple votes where a set of voters prefer two candidates over all other, while at best only one is likely to win. Both candidates have an incentive to publicly encourage voters to support the other candidate, while privately encouraging some supporters to only vote for themselves. This strategy when taken too far may cause too many defections from both candidates support so both of them lose, while avoiding defections prevents an effective choice between the two candidates. It is named after Aaron Burr in the U.S. Presidential election of 1800, by Professor Jack H. Nagel[14], where both Thomas Jefferson and Aaron Burr ran as Democratic-Republican.[15]

References
  • Behind the Ballot Box: A Citizen's guide to voting systems, Douglas J Amy, 2000. ISBN 0-275-96585-6
  • Mathematics and Democracy: Recent advances in Voting Systems and Collective choice, Bruno Simeone and Friedrich Pukelsheim Editors, 2006 ISBN 978-3-540-35603-5
  1. Bullet Voting Explained
  2. Merits Of Single-Shot Voting Questioned
  3. EDITORIAL: To plump, or not to plump your vote
  4. "Does "Bullet Voting" Really Work? - Philadelphia Magazine". Philadelphia Magazine. 2015-10-27. Retrieved 2017-07-12.
  5. "Ocean City Maryland News | OC MD Newspapers | Maryland Coast Dispatch » Merits Of Single-Shot Voting Questioned". mdcoastdispatch.com. Retrieved 2017-07-13. Single-shot voting is essentially a tactic used by voters ... choosing only one candidate or a lesser amount of candidates than open seats.
  6. "Drawing the Line". Southern Poverty Law Center. Archived from the original on 2017-02-21. Retrieved 2017-07-13. 4. Anti-single-shot provisions: These provisions compel voters to cast a vote for every open seat, even if voters do not want to support more than one candidate. A voter who casts a vote for less than the entire number of seats open (a “full slate”) will not have his or her ballot counted. Requiring minority voters to vote for a full slate dilutes their voting strength by preventing them from concentrating their support behind one candidate.
  7. Decision 1997: Constitutional Change in New York By Henrik N. Dullea, 1997
  8. Democracy in Divided Societies: Electoral Engineering for Conflict Management, Benjamin Reiley, 2001 ISBN 0521797306 p.145 ("But the Bucklin system was found to be defective, as it allowed a voter's second choice vote to help defeat a voter's first choice candidate. Under these circumstances, most voters refrained from giving second choices, and the intent of discovering which candidate was favoured by the majority was thwarted.)"
  9. Amy (2000) p.60 ('At-large voting can discourage voters from supporting all the candidates they want to see on the council, a practice called bullet voting... This is a political predicament racial minorities find themselves. They must give up all of their other votes to have any hope of electing their first choice.)
  11. The Troubling Record of Approval Voting at Dartmouth
  12. Amy (2000) p. 130. (As with at-large voting, if you choose all your votes in limited voting, there is a chance this strategy can be self-defeating... you vote may help other candidates defeat your favorite one.)
  13. "Black candidate for Euclid school board to test new voting system". Archived from the original on 2011-06-07. Retrieved 2011-06-07.
  14. The Burr Dilemma in Approval Voting Jack H. Nagel, University of Pennsylvania - Political Science
  15. Simeone and Pukelsheim (2006) p. 142 3.1 The Burr Dilemma.
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