playing the quorum game

earlier this week, Italians voted on a slate of four legislative referendums.  for each the question was to overturn a law passed by the current ruling party, led by Silvio Berlusconi.  (if you don't follow Italian politics closely, the last you heard of him he was probably either getting indicted for paying an underage prostitute or getting smashed in the face with a model of the Milan cathedral.) i found out the news because i read the headlines of La Repubblica every morning.  however, i didn't really know anything about the referendums until the day of the voting.  this is mostly due to the fact that Italian journalistic style makes it as difficult as possible to actually keep track of what's going on.  back page stories become front page stories with no fanfare, introduction, or exposition, and if you haven't been reading cover to cover (and how do you even know when it's all online?), then too bad.  add in the fact that their politics coverage reads like Variety even when it is the top story, and it can be a bit challenging.

nevertheless, it was obvious that i was looking at election results, and the key bit of news was that there was a quorum.  after a crash course on Wikipedia i found out that these votes, in order to be valid, have to have 50% turnout of all eligible voters nationwide — something like 25 million votes!

i checked back later in the day, once they'd started tallying yes and no votes, to see the percentages.  all four referendums were passing (where passing means to repeal the law) by about 95% to 5%.  this result was billed as schiacciante, 'shocking'.  

but was it really? i thought about it and realized, that no, Italians either understand or have been well-coached on how this fairly complicated electoral process works.  because of the quorum rule, there is no potential benefit in casting a "no" vote.*  once the quorum is met, a simple majority wins the contest.  so in perfect conditions, 25%+2 votes are the minimum to pass the referendum (50%+1 of eligible voters cast ballots, and of those ballots 50%+1 marked "sì").  taking the real numbers from this week's election makes the danger all the more evident.  if, for example, turnout had been a few percent different and the quorum was only 51%, the "no" votes would have contributed to passing the measures.  if they abstained, the quorum would not have been met, and the measure would fail.  that didn't happen, since an absolute majority of the electorate voted "sì" and thus guaranteed victory, but it shows just how tricky the situation was.

so was it shocking?  from a big picture, political perspective, perhaps.  maybe Italy is finally ready for some real change away from the craziness and corruption of the Berlusconi governments.  but from a game theory or strategic perspective?  not at all.  both the ayes and the nays knew exactly what they were doing, and the ayes had it.

*hypothetical exceptions:

  1. there is a historical tendency of very high voter turnout regardless of position (not improbable given Italy's 90% turnout in parliamentary elections – yes, the USA is at the absolute bottom of that table with 48%)
  2. nobody gets it and everyone who wants to vote "no" has to do so just to try and make sure that all of his dumb compatriots don't screw it up for him.  this quickly devolves into paranoia and/or a lose-lose situation.