[EM] Combating the Approval Burr dilemma

[raphfrk at netscape.net]

 As a quick recap, the Burr dilemma is where there is an incentive for voters from 
 the same faction/party not to approve all members of that party.
 
 E.g. if first choice preferences are 
 
 A1: 25%
 A2: 30%
 B: 45%
 
 A1 and A2 agree to ask their supporter to approve each other.
 
 The ballots cast are:
 
 A1: A1
 A2: A1 and A2
 B: B
 
 A1 then wins as A1's supporters defected on the agreement even 
 though A2 was the least supported candidate and a minority of 
 the A party liked the candidate. 
 
 This incentive could result in B winning if both A2 and A1's
 supporters did it, which results in a minority candidate winning.
 
 --------------------------------------------
 
 So, what about something like this:
 
 On the ballot the voter can mark a candidate as
 
 - favorite (max 1)
 - conditional
 - approved
 
 Count all ballots to determine the number of favorite votes for each
 candidate.
 
 Count all the approval votes. 
 
 A ballot counts as approving a candidate if 
 
 - the voter selects approved
 - the voter selects favorite
 - the voter selects conditional and the candidate got more favorite
 votes than the voter's favorite.
 
 --------------------------------------------
 
 If everyone using conditional or favorite, then a candidate who is the 
 favorite of the majority would always win.
 
 In the above example, the voters could cast
 
 25 A1: A1(F), A2
 30 A2: A1, A2(F)
 45 B: B(F)
 
 Results:
 
 A1: 25 (obtained fewer votes than A2 as favorite so doesn't get transfers)
 A2: 55 (full transfers)
 B: 45 
 
 A2 wins. 
 
 If the A1 voters withheld support, the result would be:
 
 A1: 25 (no transfers due to lower favorite)
 A2: 35 (no transfers as A1 voters defected)
 B: 45
 
 B wins. 
 
 Defecting will not help your favorite get elected.
 
 The system has some plurality like effects though. One option would
 be to use approval for the favorite system (so allow overvoting in the
 favorite count). In fact, it would be possible to have multiple stages,
 so use the system itself for the favorite count.
 
 I think the tactics in such a case would get pretty complex.
 
    Raphfrk
 --------------------
 Interesting site
 "what if anyone could modify the laws"
 
 www.wikocracy.com    
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