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, 2014 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, 2014 at 19:31
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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 May 22, 2014 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, 2014 at 21:34
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    electowiki.org/wiki/Negative_vote It still suffers from vote-splitting, since you are unlikely to either 1. Love one candidate while hating all the rest or 2. Hate one candidate while loving all the rest.
    – endolith
    Mar 18, 2021 at 21:00

2 Answers 2


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.

  • 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, 2014 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, 2014 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, 2014 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, 2014 at 10:01
  • I'd +1 you for the edit, but I already did.
    – Bobson
    May 28, 2014 at 17:14

Is there an obvious reason why I can't seem to Google such a system

Probably because you haven't thought to Google "range voting". This is equivalent to being allowed to assign a score of 0, 1, or 2 to each candidate (your system give -1 for "against", +1 for "for", and 0 for no vote, so candidates will differ by a constant (across candidates) score when comparing your system to a range voting system going from 0 to 2).

This would be rather tedious; you wouldn't want to skip any candidate you don't like, since doing so gives them more points than voting against them, but it means that you have to go through the entire candidate list, as opposed to "normal" voting where you can just mark one candidate and you're done. And there would be little reason to skip a candidate; it's been shown that the strategic optimum in range voting is to give each candidate the maximum or minimum score, depending on whether you think they're better or worse than the "baseline" candidate. And if everyone votes either for or against each candidate, you might as well just let leaving a candidate's name blank be interpreted as "against", and now you're right back at approval voting.

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