[EM] RE : [Fwd: Condorcet and the laternoharm criterion]
Dave Ketchum
davek at clarityconnect.com
Fri Dec 22 23:22:05 PST 2006
Seems we are more into skills in writing English, than into programming.
We have 15 voters, with an election summable as:
7C>5B  with original vote
7B>5A  unchanged
7A>5C  "  completes a cycle that is a tie.
8B>7C  modified vote that makes B winner with NO cycle.
Here we have 3 A voters, deciding that C's 1/3 chance of winning is a
disaster to avoid, work to change the odds such that, if A doesn't win,
chances are better that B, their second choice, will be the winner.
TWENTY percent of the voters making this change resulted in B winning 
true success. Disappointing that this reduced A's chances but, assuming
this was a legitimate election, they could not know where they started
from and were simply doing what they could to improve their odds.
To those who call this ugly, not near what I displayed for IRV the other
night with two voters voting for B  and thus causing A to win in place of
C  when C was liked about twice as much as A.
As to "arbitrarily close", this example's 20% change would overbalance
such a change.
DWK
On Fri, 22 Dec 2006 21:30:40 +0100 (CET)Kevin Venzke wrote:
> Michael,
>
>  mrouse1 at mrouse.com a écrit :
>
>>According to wikitest.electorama.com, laternoharm is incompatible with
>>the Condorcet criterion. Is there a general proof or a set of examples
>>illustrating this? Plus, are there any examples not involving circular
>>ties?
>
>
> Douglas Woodall showed this in "Monotonicity of singleseat preferential
> election rules," Discrete Applied Mathematics 77 (1997), pages 8687.
>
> 3 a
> 3 b
> 3 c
> 2 a>c
> 2 b>a
> 2 c>b
>
> Under Woodall's assumptions there must be a scenario "arbitrarily close"
> to this one which is not a tie. So suppose that A is the winner in such
> a scenario. If the 3 "a" voters instead vote "a>b," then B is the CW.
>
> Alternatively you could say that the original scenario is a tie that is
> won by each candidate 1/3 of the time. Then still, when the B preference
> is added, A is harmed by having his win odds go from 1/3 to 0.
>
> There is no example not involving circular ties. If you can be assured
> that every election will have a CW, there won't be any LNHarm problems.
>
> Also, you can modify this proof to make a similar demonstration about
> Condorcet and (my interpretation of) FBC.
>
> Kevin Venzke

davek at clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 138271708 6076875026
Do to no one what you would not want done to you.
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