# [EM] Steph: Extremist shouldn't change outcome?

Stephane Rouillon stephane.rouillon at sympatico.ca
Wed Feb 19 18:15:35 PST 2003

```Mike --

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.
>
>                 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.
>
>
>                 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).

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,
Steph

MIKE 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: CBA
>
> Because, 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: CBA
>
> Relative margins of the defeats:
>
> CB: (31-20)/51 = 11/51
> BA: 1/100
> AC: ((20+49)-31)/100 = 38/100
>
> BA 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: 69
>
> Condorcet(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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