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chalkdust first-preference votes is eliminated. Votes for the eliminated candidate are added to the totals of the remaining candidates based on who is ranked next on each vote. If no remaining candidates are ranked on a vote, the voter is assumed to be indifferent between them and the vote is discarded. This process continues until one candidate wins by obtaining more than half the votes. The alternative vote is, by Arrow’s theorem, not independent of irrelevant alternatives, but it is clone-proof, unlike plurality voting. Consider the example above where 9 voters changed their preference from x ≻ z ≻ y to z ≻ x ≻ y. If we run an alternative vote election here, no candidate would have a majority of first-preference votes, so candidate z would be eliminated. Candidate z’s 17 votes would then be given to x, giving x a majority. The alternative vote satisfies the majority loser condition (if a majority of voters prefer every other candidate over a given candidate, then the given candidate cannot win), whereas plurality does not. So is the alternative vote a beer system than plurality? It does have some nice properties that plurality does not have, but the opposite is also true. In order for a voting system to be consistent, we require that if we arbitrarily break the electorate into two parts and both parts of the electorate declare the same winner, then an election on the whole electorate should declare the same winner as the sub-electorates. Plurality is a consistent voting system but the alternative vote is not. Consider the example of two sets of voters and their amalgamation in Table 2, from Woodall (1994). For electorate (a), z is eliminated so x gains 0 votes and y gains 3, Australian Electoral Commission making y the winner. For electorate (b), x is eliminated so An Australian ballot paper, using the y gains 3 votes and z gains 0, making y the winner again. alternative vote system. In the election with the merged electorate (a) + (b), y is eliminated, so x gains 0 votes and z gains 8 votes, making z the winner. Voter preference x ≻y ≻z y ≻z ≻x z ≻y ≻x

Voters (a) 6 4 3

Voters (b) 3 4 6

Voters (a) + (b) 9 8 9

Table 2: Voter preferences in two electorates.


Chalkdust, Issue 03  

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