[EM] Fwd: Some chance for consensus revisited: Most simple solution

[Jobst Heitzig]

Hi Raph,

this was suggested before, but I can't remember by whom. The problem is, 
as you have noted, that the method gives everyone an incentive to reduce 
her approvals for non-favourites as long as this doesn't change the 
approval order.

For example, consider our example in which the true utilities are
    55: A(100) > C(70) >> B(0)
    45: B(100) > C(70) >> A(0).
With the suggested method, the resulting approval score of C will not be 
100 (which would be desirable and would be the result under D2MAC, e.g.) 
but would rather be only 56. This is because if it would be larger than 
56, any voter who approves of C will have an incentive to not approve of 
C as this would transfer some probability from C to her favourite.

Your 50%-modification will not change the above flaw, I'm afraid, since 
C is nobody's favourite anyway.

Yours, Jobst

Raph Frank schrieb:
> I have including the EM alias
> 
> On Mon, Feb 9, 2009 at 11:55 PM,  <fsimmons at pcc.edu> wrote:
>> I like this concept, but I'm not sure exactly how to combine it with the above
>> "tyranny free" method.  I'm sure it is worth pursuing.
> 
> I was thinking:
> 
> - Each voter marks a favourite and approved compromises
> 
> 1) Find the approval winner
> 
> 2) Place all ballots which approve that winner in a pile and assign it
> to the approval winner
> 
> 3) Repeat the process excluding any ballots which have been assigned to a pile
> 
> 4) When all the ballots are assigned to a pile, pick a ballot at random
> 
> 5) The candidate associated with the pile the ballot was picked from
> is declared the winner
> 
> Notes:
> 
> Step 4 could just be pick a pile with each pile having a weighting
> equal to the number of ballots in the pile
> 
> Piles smallers than a threshold could be excluded.  In that case, the
> voters corresponding to those piles should be allowed to reassign
> their probability.  For example, they could rank the candidates and
> their ballot would be assigned to the pile of the highest ranked
> candidate.
> 
> A bullet voter would automatically create/be assigned to a pile for
> his candidate, since he hasn't approved any other candidate, so the
> ballot cannot be assigned to a different pile.
> 
> The favourite marking doesn't actually have any effect in this method.
> 
> However, it doesn't handle the generic case well though.
> 
> 55: A(100) B(70) C(0)
> 45: A(0) B(70) C(100)
> 
> If the 45 faction votes
> 
> 5: B+C
> 40: C
> 
> and the 55 faction compromises
> 
> 55: A+B
> 
> The results are
> 
> Round 1
> A: 55
> B: 60
> C: 40
> 
> B wins,
> B pile becomes
> 5: B+C
> 55: A+B
> 
> Remaining
> 40: C
> 
> Round 2
> C wins,
> C pile becomes
> 40: C
> 
> The result is
> B: 60%
> C: 40%
> 
> By compromising, the 55 faction effectively transferred its weight
> from A to B, without the 45 faction having to respond in kind.
> 
> A rule that would help would be that a ballot can only be placed in a
> pile for a candidate who isn't the favourite on the ballot, if ballots
> with that candidate as favourite represent less than half of the
> ballots in that pile.
> 
> This would change the outcome:
> 
> 5: B+C*
> 40: C*
> 55: A*+B
> 
> The results are
> 
> Round 1
> A: 55
> B: 60
> C: 40
> 
> B wins,
> B pile becomes
> 5: B+C*
> 55: A*+B
> A* ballots are 91% of the ballots
> 
> The A favourite ballots are more than 50% of the pile, so 50 of them
> are removed to balance the pile.
> 
> B pile becomes
> 5: B+C*
> 5: A*+B
> A* ballots are 50% of the ballots
> 
> Remaining
> 50: A*+B
> 40: C
> 
> Round 2
> 
> 50: A*+B
> 40: C
> 
> A wins (B pile has already been created)
> A pile is 50: A* + B
> 
> Round 3
> 
> 40: C
> 
> C wins
> C pile is 40: C
> 
> Result
> 
> A: 50%
> B: 10%
> C: 40%
> 
> The 50% rule means that the 55 faction has effectively said that they
> will only move one ballot from A to B for every ballot the 45 faction
> moves from C to B.
> 
> If both factions were to compromise, the result would be
> 
> B wins round 1 and has pile
> 55: A*+B
> 45: B+C*
> 
> 10 A*+B ballots are removed to make it 50%
> 
> B pile
> 45: A*+B
> 45: B+C*
> 
> Remainder
> 10: A*+B
> 
> Remainder goes to A's pile.
> 
> Result:
> 90%: B
> 10%: A
> 
> This is reasonably fair, as it recognises the fact that faction A is larger.
> 
> Also, it is an improvement over the previous non-compromise result
> from the perspective of both factions.
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