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On small parties and strategic voting: Burn your vote

While arguments against voting for smaller parties that are unlikely to cross the minimum threshold tend to be erroneous, don’t fall into the trap of thinking your vote actually determines what happens here over the next four years – for that you need a different type of democracy.

By Tomer Zeigerman

Asma Agbaria, chairwoman of Da’am (YouTube screenshot)

In the unappealing lineup of political parties competing in today’s elections, Da’am stands out as a genuine alternative, a promise for Arab Jewish cooperation that is more than just lip service. Yet the party received only 2,645 votes in the last elections and despite an apparent surge in its popularity, is by no means a lock to receive enough votes this time around to pass the threshold for Knesset representation (about 70,000 votes). And so ‘why burn your vote?’ is what you’ll inevitably hear if you mention you are considering voting for a small party like Da’am.

This line of thinking implies that voting is strategic act – that the individual decision about whom to vote for has an effect on the outcome of an election, and that it is therefore advisable to choose a larger party – to be guaranteed representation, to reinforce that (larger) party, and to add one more vote for the political camp that party belongs to. ‘A vote for Da’am (or any leftist party that may not get seats in the Knesset) is a vote for the Right’ is another common refrain.

It is an erroneous argument on all counts. From any one individual perspective, a single vote has no effect on the outcome. The probability of a given vote being decisive in a closely contested election has been calculated at 8.1079 X 10-9 (about one in 8 billion). Strategic voting, too, is pointless – changing your vote from one party to the next will not measurably affect the outcome any which way. Here, rational choice theorists (who know that the costs of voting always outweigh the infinitesimal utility of that act) and radical democrats (who deride the notion that voting in representative systems might be considered a political-democratic act) are in complete agreement – when considered in reference to its outcome, voting has no political significance.

But what if we look at the aggregate rather than the individual perspective? After all, it’s not about just my vote, it’s about what everyone does – if the tens of thousands who cast their ballots for parties that do not receive enough votes to be represented in the Knesset all chose bigger parties instead, then these parties would gain more seats. And this could determine whether the Right or the Left has the larger bloc in the Knesset.

This reasoning also fails. Firstly, it suffers from the false assumption that my own action determines the way everyone will act – that if I choose not to vote for a certain party for fear of wasting my vote everyone else will also choose to avoid voting for them. Yet, of course, in the voting booth you only control your own actions. Your decision does not affect anyone else’s.

But even if it was possible to influence everyone facing the same dilemma to vote the same way, say if your posts on social media were so persuasive as to deter everyone else from voting for parties unlikely to pass the threshold, if you could manage to coordinate such an effort on a larger scale then your actions would still not have that great an effect on the ultimate outcome of the elections. In a recent blog post, statistician Yosi Levy ran the possible scenarios. He found that in the previous Israeli elections, even if all the votes that were ‘lost’ due to (leftist) parties not passing the threshold would have gone to larger parties instead, this would not have been enough to substantially affect the outcome of the elections.

If voting – strategicly or otherwise – does not matter, why vote at all? A tricky question, given that your vote has such little chance of determining the outcome. In fact most ‘experts’ struggle to account for why any individual should bother to vote at all, aside from social compulsion. But if we look at other reasons beyond affecting the final outcome, we might find possible answers – for example, using the voting process itself to make a political statement. This is the reasoning behind the ‘Real Democracy’ initiative. Obviously a symbolic gesture, it is nonetheless an avenue for a different kind of politics. Finally, you might vote simply because you believe in the particular party you are supporting – certainly a better idea than ineffectual strategic voting. Just don’t fall into the trap of thinking your vote actually determines what happens here over the next four years – for that you need a different type of democracy.

Tomer Zeigerman is a PhD candidate in Political Theory at the New School for Social Research and is currently residing in Israel.

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    1. anonymous moose

      Tomer, I’m pretty sure you’re wrong about the mathematical part of the argument. I’m a mathematician and a leftist (voted Hadash) if it matters.

      You write “The probability of a given vote being decisive in a closely contested election has been calculated at 8.1079 X 10-9 “. I actually skimmed the article you quote and found the relevant part (where he quotes Myerson, 2000), and I can tell you that it is flawed. The author interprets the phrase “closely contested” in a patently flawed way. I can explain here (or over email, if you want) in case there is interest, but I can tell you that the number he gives is way off the mark, and I’m pretty sure he doesn’t understand that what he’s doing is flawed.

      Instead of giving the details here, I’ll just give the actual number (and, again, feel free to ask for more details): the chance of a single vote being significant in a closely contested election of 4 million people varies between 1/40,000 and 1/2,000, depending on how you define “closely contested”. These are still small numbers: for example, if you would be willing to pay, say, 20,000NIS to change the ruling party, then you shouldn’t be willing to pay more than 10 shekels or so for the transportation to the ballot office. (The chance to make a difference becomes even lower when we consider a multi-party system in a non-highly-contested election such as the current one.)

      I don’t have any well-reasoned criticism on the rest of the post, although I did get the uneasy feeling while reading it, that you’re ignoring the game theory of the situation. This is one thing that people seem to do surprisingly well: they ask “what if a lot of people reasoned like me and acted like me?” and the results of this question gives them motivation for strategic voting, which is actually good in a game-theory perspective because people *should* be voting strategically if they are rational. In any case, I think you’re discounting too much the actual effects of voting and sticking too much to the claim that individual votes don’t matter, although I struggle to mount a detailed criticism of your post regarding this point.

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      • Kent


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    2. Tomer

      Thanks for the comments AM. I went ahead and looked at some other approaches of determining the probability that a single vote is decisive – there are widely divergent estimates, based on different assumptions made by authors(e.g. here http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1265.pdf and there are many others). Most assumptions do not apply to the Israeli case, where we need to focus not on the probability of your vote deciding which of the candidates will be PM (as we are seeing now, this is not strictly determined by the distribution of seats in the Knesset: i.e. even if Yesh Atid gained one more seat, and the center left bloc had 61 seats, there is still a decent chance Bibi would have ended up as PM). Instead we need to determine the probability that either 1. (you do not vote/vote for tiny party) and the larger party you would have voted for misses out on a seat by exactly one vote. 2. (don’t vote/tiny party) and the larger party misses out on a seat by exactly one vote due to the Bader-Offer surplus vote rules. I’d be happy to know your thoughts on this.

      -I do not see how the question “what if a lot of people reasoned like me and acted like me?” leads to strategic voting. The rational person (assumed by game theory) knows that this question is irrelevant unless you can directly influence, through your action, what other people will do (i.e. if by not voting you somehow cause many other people to abstain as well). There is something to be said for wisdom of the crowds here, but that concept in itself still does not explain why people would be motivated to vote.

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