# [EM] RE : [Fwd: Condorcet and the later-no-harm 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, later-no-harm 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 single-seat preferential
> election rules," Discrete Applied Mathematics 77 (1997), pages 86-87.
>
> 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  13827-1708   607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.

```