Bullet voting

A voter marking a ballot for a single favorite candidate.

A bullet, single-shot, or plump vote is a ballot where an elector shows strong support for a single, favorite candidate by only ranking them.

Bullet voting can also refer to strategic truncation, i.e. declining to state lower preferences to keep a disliked alternative from winning. Every voting method failing either later-no-harm (such as approval voting) or participation (such as instant-runoff voting) will encourage bullet voting or truncation in some situations.

In later-no-harm systems, voters can use bullet voting to maximize the chances their favorite candidate will be elected, at the cost of reducing the chances that one of their later preferences will win.

In non-participatory systems (such as instant-runoff voting), voters can strategically bullet-vote to hide their support for additional candidates, as systems like IRV can cause candidates to lose if they receive too much support from voters.

In cumulative voting (a semi-proportional variant of score voting), bullet voting is encouraged and often used by minority groups to achieve proportional representation, by encouraging small groups to concentrate all their support on one candidate. During the Jim Crow era, municipalities often banned bullet voting in an attempt to prevent black voters from being able to achieve representation on city councils.

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 favorite, so it 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 favorite.

Traditional Bucklin voting, which used ranked ballots, was infamous for its high vulnerability to bullet voting due to its poor choice of ballot. Modern variants substantially reduce the problem by allowing voters to give independent ratings to each candidate separately,

Multiple winner elections

N seat elections

System	Votes
Approval voting Range voting Borda voting	Point scores
Plurality-at-large voting	N
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:

Multiple non-transferable vote methods

• 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. 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 favorite candidates to avoid being locked out of the election entirely.
  • Range voting is a generalization of Approval voting where voters can give gradations of support for each candidate. Here bullet voting refers to providing 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 three votes for the first, two for the second, and one for the third choice. This encourages minority voters to bullet vote (not using all the rankings). If voters are required to rank all the candidates, it further encourages voters to (insincerely) bury strongest rivals at the lowest rankings.
• 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 the first choice. A united majority of voters in plurality-at-large can control all the winners despite any strategic bullet voting by a united minority.

Bullet voting in Cumulative voting allows multiple votes for one candidate.

Limited-Vote Systems

• 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.

• Cumulative voting allows 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.

• Single transferable vote removes the incentive for sincere strategic bullet voting, since lower rankings are only used later (after higher choices have been elected or eliminated). However, it creates an incentive for insincere bullet voting in situations where adding additional preferences would hurt later candidates; in some situations, adding a later preference can cause that later-preference candidate to lose.

See also

• Burr dilemma

Further reading

• 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