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Voting matters - Issue 12, November 2000

Mixing X-voting and preference voting

I D Hill

Hugh Warren[1] puts forward a plan to incorporate X-voting into an STV election, so that those who prefer it are not forced into STV against their will. The aim is very sensible but, as he says, the voters must 'be assured that it is being done in a fair way'. As Hamlet said: 'ay, there's the rub'. Is it possible to find a way that actually is fair and, equally necessary, will be accepted as fair by those concerned?

The Warren suggestion is to treat Xs as equal first preferences, treating each X as worth 1/m where there are m places to be filled. Now suppose, as he does, that m = 10. If two voters each plump for a single candidate, one using an X and the other using a 1 in marking the paper, would it be regarded as fair for the second of those to be treated as worth 10 times as much as the first? Surely not.

In an editorial footnote, Brian Wichmann suggests an alternative formulation, treating each X as worth 1/n where n is the number of Xs marked on the paper. That would solve the above difficulty, but only at the expense of introducing a new one.

Suppose two candidates get X-votes only, one getting 20 Xs each of value 0.5, because those voters used two Xs each, the other getting 40 Xs each of value 0.2, because those voters used five Xs each. The first then has a total vote value of 10, the second a total vote value of 8. So if one of the two is elected it will be the one getting 20 Xs, not the one getting 40 Xs. Would X-voters regard that as fair? I am quite sure that they would not. It is just this sort of situation that I presume that the Warren formulation was carefully designed to avoid. Is there any way of doing it that everyone would think fair in all cases? I doubt it.


  1. C H E Warren. Incorporating X-voting into Preference voting by STV. Voting matters, Issue 11, p2. 2000.

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