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I've been reading about tactical voting - often it happens when a voter is more motivated to avoid one candidate than elect another. Tactical voting is considered a risk for many voting systems, or at least a manipulation of their original intent. I wonder what the consequences for voting behaviour would be if the option to express disapproval was made explicit.

What about if voters had a single vote which they could cast either for one candidate or against another, but not both? Sum them for each candidate and subtract the latter from the former, highest final score wins.

Has anybody made predictions, conducted simulations etc. on how mass voting behaviour would play out in such a system? Is there an obvious reason why I can't seem to Google such a system, whereas standard single non-transferable vote and disapproval vote (of which I am proposing a simple combination) have been much discussed? Is there something trivially 'wrong' with it? Am I right in thinking it could eliminate tactical voting?

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    Interesting question, but it's kindof buried in there. Can you trim this down a bit and/or format it so that the key points stand out? – Bobson May 22 '14 at 14:32
  • Hey, I will trim accordingly. Most SE sites I've used before value 'well researched' questions to demonstrate it's not an easily google-able topic. Also I wanted to head off stock answers about disapproval voting, because that's not what I'm talking about. – benxyzzy May 22 '14 at 19:31
  • @benxyzzy trying to head off stock answers and showing your research is great, and they're an important part of narrowing down your question to the bits that you're interested in. You just need to think about whether what you're telling us actually helps readers identify and narrow down the question. If it doesn't, than it's just noise and there's no need to include it. – Sam I am says Reinstate Monica May 22 '14 at 19:56
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    This would be awesome... except I can totally see some elections in the US that the winner is the one with the higher negative total – SoylentGray May 22 '14 at 20:19
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    @Chad I personally expect the winner would have both the most "for" votes and "against" votes in the majority of elections (yet still winning after subtraction of the latter from the former). You can predict the newspaper headlines as something like "party with most 'no' votes wins", but I see no problem with this. In fact I believe that's how it actually works right now. Only difference is, the 'no' votes are currently an inexact science involving future-mindreading on the part of voters and past-mindreading on the part of analysts who want to to interpret the outcome. – benxyzzy May 22 '14 at 21:34
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Consider the following case: approximately 500 people are of type A, B, C

Type A prefers candidate A to B to C Type B prefers candidate B to C to A Type C prefers candidate C to A to B

So the society as a whole prefers A to B, C to A, and B to C. If all players pick down-voting their least favourite candidate, then the winner will be the least hated one (for example let's say A=-500 b=-501 c=-502| ). This, however, is not a nash equilibrium because forward looking voters of type C would rather change their vote from down-voting B to up voting C (A=-500,B=0,C=2). This would change the winner to C (and is the very type of strategic voting the system sought to avoid). This new voting pattern, however, is also not an equilibrium, because forward looking voters of type B would then rather swing their votes from down voting down A to voting up B (A=0,B=500,C=2). And then C would rather switch its votes to down voting B (A=0,B=-1,C=-502). WIP

The winner, however, will still be rather random, and the decision to down or up vote is still a tactical decision that will determine that winner.

The fundamental problems is Condorcet's paradox, which is caused by the emergence of intransitive preferences when the majority makes decisions.

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  • Good answer. Can you elaborate on the example a bit more, though? Something like "If x people vote this way, A wins, but if they vote this other way, C wins". – Bobson May 23 '14 at 13:23
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    @Bobson I actually thought about my example more and my statement "Your voting system seems to simplify the choice, either down-vote the one you like the least or up-vote the one you like the most." is wrong, but I think "The winner, however, will still be rather random, and the decision to down or up vote is still a tactical decision that will determine that winner" is still right. I will rework this when I have time. – lazarusL May 23 '14 at 14:11
  • Concorcet's paradox and intransivity appear to be an issue for all the other voting systems as much as this one (even 'democracy' as a whole, as your last link puts it). The canonical A/B/C example looks like a critique of ranked voting - in which case, if all candidates are being ordered it doesn't matter whether the vote is "for" or "against" (they're functionally equivalent: just flip the list). – benxyzzy May 24 '14 at 9:50
  • Sorry, hit return by accident and 5min edit limit timed out. ... Simplification was what I was interested in, and the choice of approval/disapproval (though still tactical in a very semantic sense) seems much easier to analyze than current tactical voting behaviour. Your links suggest no voting system could overcome the paradox or intransivity. – benxyzzy May 24 '14 at 10:01
  • I'd +1 you for the edit, but I already did. – Bobson May 28 '14 at 17:14

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