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The Borda count (named after Jean-Charles de Borda) is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all votes have been counted the candidate with the most points is the winner. Because it sometimes elects broadly acceptable candidates, rather than those preferred by the majority, the Borda count is often described as a consensus-based electoral system, rather than a majoritarian one.

Voting and counting

Under the Borda count the voter ranks the list of candidates in order of preference. So, for example, the voter gives a '1' to their first preference, a '2' to their second preference, and so on. The number of points given to candidates for each ranking is determined by the number of candidates standing in the election. Thus, under the simplest form of the Borda count, if there are five candidates in an election then a candidate will receive five points each time they are ranked first, four for being ranked second, and so on, with a candidate receiving 1 point for being ranked last (or left unranked).

When all votes have been counted, and the points added up, the candidate with most points wins.

Example 1

Example with (4,3,2,1) points awarded:

1) maurice - voting for (Yuli, Araver, Hirkala, maurice)
2) Yuli - voting for (Hirkala, Araver, maurice, Yuli)
3) araver - voting for (Maurice, Hirkala, Yuli, Araver)
4) Hirkala - voting for (Araver, Yuli, maurice, Hirkala)

is tallied as follows

1) maurice - 1+2+4+2 = 9
2) Yuli - 4+1+2+3 = 10
3) Araver - 3+3+1+4 = 11
4) Hirkala - 2+4+3+1 = 10

resulting in a lynch of Araver. The normal first-option voting would have resulted in a 4-way tie.

Example 2

Example:

1) maurice - voting for (Yuli, Araver, maurice)
2) Yuli - voting for (Araver, maurice, Yuli)
3) araver - voting for (Maurice, Yuli, Araver)

is tallied as a three-way tie, same as normal first-option voting.

Truncated voting

A common way in which versions of the Borda count differ is the method for dealing with truncated ballots, that is, ballots on which a voter has not expressed a full list of preferences. There are several methods:

  • The simplest method is to allow voters to rank as many or as few candidates as they wish, but simply give every unranked candidate the minimum number of points. For example, if there are 10 candidates, and a voter votes for candidate A first and candidate B second, leaving everyone else unranked, candidate A receives 9 or 10 points (depending on the formula used), candidate B receives 8 or 9 points, and all other candidates receive either zero or 1. However, this method allows strategic voting in the form of bullet voting: voting for only one candidate and leaving every other candidate unranked.
  • Voters can simply be obliged to rank all candidates.
  • Voters can be permitted to rank only a subset of the total number of candidates but obliged to rank all of those, with all unranked candidates being given zero points.

Tactical manipulation

Tactical voting

Like all voting systems, the Borda count is vulnerable to tactical voting. In particular, it is highly vulnerable to the tactics of compromising and burying:

  • Compromising: voters can help avoid the election of a less-preferred candidate by insincerely raising the position of a more-preferred candidate on their ballot.
  • Burying: voters can help a more-preferred candidate by insincerely lowering the position of a less-preferred candidate on their ballot.

An effective tactic is to combine these two strategies. For example, if there are two candidates whom a voter considers to be the most likely to win, the voter can maximise his impact on the contest between these front runners by ranking the candidate whom he likes more in first place, and ranking the candidate whom he likes less in last place. If neither front runner is his sincere first or last choice, the voter is employing both the compromising and burying tactics at once; if many voters employ such strategies, then the result will no longer reflect the sincere preferences of the electorate.

However, some research (a mathematical framework for evaluating positional methods) claims that the Borda count has fewer opportunities for tactical voting than other positional methods such as plurality voting.

Strategic nomination

The Borda count is highly vulnerable to a form of strategic nomination called teaming or cloning. This means that when more candidates run with similar ideologies, the probability of one of those candidates winning increases. Therefore, under the Borda count, it is to a faction's advantage to run as many candidates in that faction as they can. For example, even in a single-seat election, it would be to the advantage of a political party to stand as many candidates as possible in an election. In this respect, the Borda count differs from many other single-winner systems, such as the 'first past the post' plurality system, in which a political faction is disadvantaged by running too many candidates. Under systems such as plurality, 'splitting' a party's vote in this way can lead to the spoiler effect, which harms the chances of any of a faction's candidates being elected.

Mafia Borda voting

Proposed rules

Borda voting has not yet been used in Mafia games, however it was proposed by maurice and will be implemented by Yuli in one of his upcoming Mafias. This would replace the normal plurality voting system, using a similar roster voting format.

Proposed rules (Truncated Borda voting with 3 options for N>3 players):

  1. All players must rank three players, else vote is nullified
  2. "no lynch" is allowed
  3. Point system is (3,2,1) (first choice, second choice, third choice).

Discussions

There is an apparent reversal of roles:

  • Borda count is used for electing the most preferred candidate
  • Mafia Borda voting is used to eliminate a player from the game = selecting the most un-liked candidate out of all.

While mathematically, the situations are symmetrical, underlying psychological or social interference is expected.

The effect of the known tactical manipulation strategies of the Borda count on the Mafia Borda voting system is unknown. The "Strategic Nomination" manipulation strategies does not apply directly, since the number of candidates is fixed, but it does imply that split Baddie suspects may have a bigger chance to get lynched than when using Mafia plurality voting.

The effect of the tie lynch rules is also unknown / not estimated to date.

See also

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