Algorithmic Asset Voting: Difference between revisions

(refs heading)
Line 53:
== Lewis Carroll's own likely observations that Asset is intended to be Condorcet-efficient ==
Lewis Carroll is the first known inventor of Asset Voting. In a passage in an article<ref>[https://www.rangevoting.org/BlackCarrollAER2.pdf Lewis Carroll and the Theory of Games, Duncan Black] (starting at the sentence "Suppose we have a multimember constituency..." on Page 4 and ending at the sentence "In general, however, an operational answer to the problem is again not feasible." on Page 5)</ref> describing his thought process in developing Asset, Carroll appears to have noted that the ideal PR scheme would involve voters forming into sets of coalitions, and then, when enough voters prefer a different set of coalitions than the one that is currently formed, a different set of coalitions is formed, and this repeats until no more improvement is possible. He also notes that it is possible to, by looking at ranked ballots, figure out what sets of coalitions might occur if the voters were acting "rationally" (most likely meaning maximally strategically), and he even solves a few examples where such an approach yields different results from STV, though it is noted that at the time, the full computation for this process when looking at the ballots for a large-scale election would've been "indeterminate". This all appears to establish that Carroll was interested in finding a Condorcet equilibrium for the final set of winners, and saw Asset as the easiest way to do it, because he believed the candidates' preferences would be close enough to the voters' preferences to make the candidates' Condorcet equilibrium more Condorcet-efficient by voter preference standards than STV.
 
== Notes ==
It could be possible for a voter to submit a ballot indicating partial preferences in certain pairwise matchups i.e. that they'd want to only give 0.2 votes to help Candidate A be in the winner set rather than candidate B, but 1 full vote to help Candidate A and/or B be in the winner set over Candidate C. So for example, if they voted with a rated ballot A10>B8, A10>C0 and B10>C0. See the "connections to cardinal methods" section of the Condorcet methods page for more information. Note that this may be possible even in the multiwinner case.
 
The use of the [[KP transform]] on rated ballots and then converting those Approval ballots to ranked ballots allows voters to submit, for example, a rated ballot A5 B4 C3, and have it treated either as 0.2 votes A>B, 0.2 votes B>C, and 0.4 votes A>C (score for preferred candidate minus score for less preferred candidate divided by max score yields the number of votes in each matchup) or 1 vote A>B, 1 vote B>C, 1 vote A>C.
 
 
 
 
== References ==