[EM] Helping a candidate in the case of ties

[Juho]

How about defining the positions as follows.

A>B>C => A=1, B=2, C=3

A=B>C => A=1.5, B=1.5, C=3

A's position got worse in the second example. B's position got better.

Juho


On Nov 24, 2009, at 6:51 PM, Kristofer Munsterhjelm wrote:

> It's fairly straightforward to define whether a candidate is helped  
> after a change of ballots if "helping" is limited to win/not win: if  
> the candidate wasn't in the set of winners (ranked first on the  
> social ordering), but is after the modification, the candidate was  
> helped. It is also not that difficult to define it for a social  
> ordering without ties: if the candidate moves from qth place to pth  
> place, p < q, then he was helped.
>
> But how would one define this for an ordering with ties? The problem  
> with defining it in terms of candidates higher ranked is that if
> A > B > C > D = E turns into A > B = E > C > D, C is "helped"  
> according to that metric, even though intuitively it seems like he's  
> not so. On the other hand, defining it in terms of ranks above the  
> set containing the candidate has problems when the possible number  
> of sets change. For instance, A > B > C > D turning into A = B = D >  
> C doesn't seem to have "helped" C, although now he's second, whereas  
> before the change, he was third.
>
> Is there any consistent way of defning help and harm, in the context  
> of candidates, when the social ordering may contain ties?
> ----
> Election-Methods mailing list - see http://electorama.com/em for  
> list info