|A genuine Slovak portable ballot box.|
(Photo: Lišiak/Wikimedia Commons)
Voters in Slovakia rejected three referenda asking voters to ban same-sex marriage, adoption by same-sex couples, and compulsory sex education yesterday.
Referenda in Slovakia are only legally binding if 50 percent of eligible voters—in this case, 2,205,765 out of 4,411,529 voters—actually cast a ballot. So while more than 90 percent of people who voted on the ballot questions voted “yes,” voter turnout was less than 22 percent. With insufficient turnout, the referenda won’t take effect.
This was the strategy adopted by LGBT activists in Slovakia: rather than asking voters to vote “no,” they urged voters not to cast a ballot at all. It’s a sound strategy, because—assuming everybody who wants to reject the referenda is on the same page—voting “no” can only improve the chances of the referenda passing.
For convenience’s sake, let’s say there are exactly four million eligible voters in Slovakia. If 1,999,999 voters vote “yes” on a referendum, and nobody votes “no,” the referendum is rejected due to insufficient turnout.
But if 1,999,999 voters vote “yes” and one person votes “no,” the referendum passes.
In fact, the theoretical smallest number of “yes” votes required for passage in this example would be 1,000,001—assuming 999,999 people voted “no.”
In the case of this past vote, it looks like Slovaks who wanted to reject the referenda were on the same page and mostly stayed home instead of voting “no.” But there’s an interesting bit of game theory involved with deciding whether to stay home or to cast a “no” ballot:
Assuming you think your fellow referendum-rejecters are completely rational, it’s obviously best to stay home and not vote at all.
But if you think enough of your referendum-rejecters haven’t thought it through and will show up to vote “no”—enough to push turnout over 50 percent but not enough to make up 50 percent of those who do vote—then you need to show up to vote “no,” so that the “no” vote has a fighting chance of winning.
But then if you don’t necessarily think referendum-rejecters are stupidly going to vote “no,” but you think enough referendum-rejecters think that enough referendum-rejecters are stupid enough to vote “no” and will subsequently vote “no” themselves, then you need to vote “no” as well. Which is bananas, right?
And there’s another wrinkle to this, too. These three referenda are bundled together on the same ballot. If blank responses—that is, checking neither “yes” nor “no”—count toward the turnout tally, that may explain why those who voted “no” did so: it’s not stupidity, but rather, a split ballot. They may have very strongly wanted to vote “yes” on one question (say, banning compulsory sex education) but weren’t in favor of another (like banning same-sex adoption). Since they’re contributing to the turnout even if they leave the adoption ban question blank, they decide to vote “no.” Which is yet another factor in the game theory calculus for referendum-rejecters—are there enough ballot splitters to push turnout over 50 percent?
In this particular ballot, the questions deal with related topics, and there’s a good chance that “yes” voters will vote “yes” for all three, and “no” voters will do the same. But there’s plenty of opportunity for monkeyshines in this setup—what if the questions were phrased differently, like asking voters to ban same-sex marriage (so that the “no” vote is the pro-LGBT vote) in one question and approve same-sex adoption (so that the “yes” vote is the pro-LGBT vote) in another?
Or what if they bundled together unrelated questions that could scramble voting coalitions? I don’t know anything about Slovak politics, but if this referendum system were in place in the United States, it’d be hard to figure out the correct strategy if the ballot questions concerned, say, mandatory vaccination, gun control, and marijuana legalization.
In any case, it highlights a quirk of democracy—that the way you let people vote can play a huge role in how that vote ends up. An ideal voting method is one in which no game theory is required as a voter; you merely express how you feel without worrying about what other people are doing.
But that rarely happens. As a result, it’s worth remembering that who’s designing our ballots can be just as important as what’s on them.