# [EM] Allowing write-ins in individual pairwise contests

Kevin Venzke stepjak at yahoo.fr
Sat Oct 19 11:45:50 PDT 2013

```Hello,

Suppose that in each pairwise contest between some X and some Y, those voters with no preference between X and Y are counted as "writing in" their first preference, thus creating a possibility that the winner of the contest is neither X nor Y, but some write-in candidate Z.

This would mean that any candidate disqualified by the Plurality criterion wouldn't win any pairwise contests.

Using this as a criterion (i.e. "you must win at least one such contest"), we can avoid the concept of "votes in total" in the definition.

If we don't want a sensitivity to the clone issues involved in using first preferences, say instead that each pairwise contest is an Approval election in which every voter approves the better of X and Y (if a preference exists), as well as all candidates deemed strictly preferable to both. (The fact that Approval's outcome depends on truncation thresholds doesn't seem to create inelegance here, as the thresholds are imposed on the voters based on the specific contest.)

(Another way to state the Approval version: X pairwise beats Y if v[x,y]>v[y,x] and v[x,y]>v[z,{x,y}] for any third candidate Z, this last term referring to voters who prefer Z to both X and Y.)

Compared to "Pairwise Plurality" (i.e. you must lose if your max pairwise votes-against-you exceeds your max votes-for-you), these are weaker. In particular, PP implies SDSC, and these criteria definitely don't.

But all of these are easiest to explain given the concept of pairwise comparisons, which is unfortunate because they themselves need to be justified, and that may not be easy. A standard pairwise contest tells you simply who would win in a two-way race. On its face it's not clear that this is even of any interest or relevance to a multi-candidate election.

I can imagine using FPP as a "base" election method, under which we recognize that strategic voters could use favorite betrayal to secure preferable results over worse ones. So if X pairwise beats Y, you know that even if the Y>X voters elevate (if necessary) Y to the top position, there are a greater number of votes of the opposite persuasion who would want to respond in kind. (Though cycles can complicate the actual incentives.) And if they were to do that, it would be impossible for Y to win the FPP contest. So when you let Y and X voters employ their lower preferences as much as possible, the ultimate method winner can't be Y. If it is, the X>Y voters feel they weren't given equal opportunity, disagree with the outcome, etc.

But, given that FPP is the base method, shouldn't upset X>Y voters have to show that the "favorite betrayal race" between X and Y ends not just in a Y defeat but in an X win? If it doesn't, then we don't know what X voters actually want and we can't say that a Y win would make anyone feel cheated. The X>Y contest is uninformative.

So the motivation behind the "pairwise write-in" concept is that they tie to this concrete setting where I can see which outcomes might actually upset people.

There's a limitation to this explanation in that I'm simply assuming that FPP is the base method according to which the voters are judging which outcomes are or aren't achievable. I'm pretty sure a different base method would permit similar analogies though. And I don't really see how even standard pairwise comparisons can be justified without slipping into describing hypothetical scenarios.

Kevin Venzke

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