[EM] Helping a candidate in the case of ties

[Kristofer Munsterhjelm]

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?