http://groups.yahoo.com/group/election-methods-list/message/10742
As for a complete mathematical and thorough definition of > reciprocal fairness, try this. > > Suppose two sets, S1 the set of voters and S2 the set of candidates. > Suppose an electoral method that produces scores for each candidate. > If you can split S1 in |S2| subsets each of a cardinality equal to the score > obtained > by the corresponding candidate, you can link these two sets using a > bijective > mapping. Each voter contributes to one and only one candidate. > If an electoral method produces scores that verify this property, > it respects reciprocal fairness.
Mike's answer is below...Using methods that verify my criteria, adding a new candidate should only affect the two neighbour subsets because this new candidate would represent better the idea of these voters in the available ranges of ranking. Using other methos like approval no. Because the new comer could have the exact balanced position that maximises the acceptance of its two neighbour groups (and even groups further with approval). On the other side of the rainbow, other voters will change their mind reacting to this new possibility. It highers the possibility of the first side finding their optimal agreement, so the second side HAS to play it safer and will conceide by accepting a more "median" or centrist candidate.Use Alex or Bart strategy with utilities, the maths confirm. > The point that I wanted to make yesterday was this: > > Either you justify your criterion in terms of other standards, and > ultimately in terms of standard that others accept as fundmental, > or you just hope that people will accept your criterion itself as > a fundamental standard. The latter isn't at all likely, and so I repeat: > Can you or can you not justify your criterion in terms of something > that others accept as fundamental? > > By the way: Of course for a public proposal, a criterion that can only > be written in mathematical language is quite useless. For something > more usable, then, you'd have to write it in English (or French, Esperanto, > etc.). If you write it in French, I'd have to find a translator, but I'd be > willing to do that. Your previoius reference to your criterion didn't tell > nearly enough about it to be a definition. > > But never mind > that. The question is whether or not you can justify your criterion > in terms of some standard that an appreciable number of people accept > as fundamental. > > Mike Ossipoff The result is: methods that do not respect the "reciprocal fairness" criteria are extremist-candidate-dependent. It is understandable that when you put a new median candidate, it could become the winner. But adding a very left candidate should not affect the right candidates results. But if adding a new candidate C makes the winner move from A to B, I think it is a fundamental bias. "Reciprocal fairness" is mandatory. It is not sufficient to ensure a fair election. The same problem can arise from vote splitting. To put it in words you like. Putting a Nader candidate should not afect the Gore-Bush result. With plurality it does because of vot splitting. With approval it would, because anti-Nader people (We, especially you, can think they are wrong, but it does not stop them from existing and voting) would add G.W. Bush on their ballot. You can argue that in this specific case the polls should have shown everybody that Nader had no chance. What if he had one? And, as fairer models will attract more candidates, the run will be tighter and these problem will rise more often. I let you answer. Steph.I was busy but I pick up where we left.
B (51) > A (49)
On a unidimensional model, an extreme candidate (C) goes before B or after A
So sincere rankings can be (C>B>A and A>B>C) or (B>A>C and C>A>B).
Please tell me where C is placed with your "sincere rankings"...It would seem that your example is not plausible at all...
In addition, let me tell you again that approval is definitively
a bad method that can elect a Condorcet Looser (if I am right,
even a strong one with 50% defeats against any other candidates even with using
Bart's optimal strategy)
See my previous posts about that.Sincerely,
StephMIKE OSSIPOFF a écrit :
Steph--Say the voting system is Condorcet with relative margins. Say
there are initially 2 candidates, A & B. 51% prefer B to A, and
so, as would any rank method, rm elects B.Now we add an extreme candidate, C. The A voters don't consider
C to be a serious rival. They believe, rightly it turns out,
that A will pairwise-beat C.Here are the sincere rankings now:
49: ABC
20: BAC
31: CBABecause, as I said, the A voters believe that A will pairwise-beat
C, they don't feel that they need to help B. And so they aren't
inclined to help B become BeatsAll winner. They don't rank B.49: A
20: BAC
31: CBARelative margins of the defeats:
CB: (31-20)/51 = 11/51
BA: 1/100
AC: ((20+49)-31)/100 = 38/100BA has the lowest relative margin, and so A wins.
What would have happened in Condorcet(wv)?
The defeat's wv:
CB: 31
BA: 51
AC: 69Condorcet(wv) has met your standard better than Condorcet(rm).
What would happen in Approval?:
B is middle, and the middle voters have no good reason to vote
for other than their favorite.Depending on which extreme appears more likely to outpoll the other,
the extreme voters on one side need Middle, to avoid their last
choice. The side that expects to be outpolled by the opposite extreme
isn't going to also expect to have a majority. They vote for Middle,
which is B. And B wins.It would seem that in this plausible example, your relative margins
is the method that lets the addition of the extreme candidate change
the outcome.Mike Ossipoff
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