# How To Vote Mathematically!

[This is a back issue of one of this site’s newsletters]

About half of you reading this are from the United States. At least, that’s my guess, based on my website‘s traffic statistics.

About a quarter – half of that half – will be voting in the coming Presidential Election, or have already done so. At least, that’s my guess, based on turnout stats I skim-read on Wikipedia.

About a half of you voting will vote for Trump, and a very slightly larger half will vote for CLinton – at least, that’s my guess, based on the latest polling data, collated by Nate Silver.

And, based on the candidates’ approval ratings – amongst the lowest in recent history – about half of you really don’t like the person you’ll end up voting for.

(Actually, I’d kind of like to check my guesses – so here’s a little poll, if you have a minute to spare… I’ll let you know next week how it went…)

Why do people vote for people they don’t want elected? It sounds silly, but really it’s not.

Imagine, for example, you’re a young single, choosing a life partner. Do you pick the guy or gal who’s good enough; who, for all their imperfections, you can see yourself sharing a life with; or do you wait for that Miss or Mr Perfect, and end up with nobody?

It makes perfect sense to choose an imperfect life partner over someone better you really have no chance with. Likewise, it makes perfect sense to vote for a less worse candidate, when you know your preferred candidate will lose.

In the United States electoral system, if your most preferred candidate has no chance of winning, then voting for them is the same as not voting. Unless you happen to be in Utah (so, about 1 of you reading this), voting for anyone other than Clinton or Trump is equivalent to not voting at all; at least in terms of the actual outcome of the presidential election. Your question on November 8 is not “which of these candidates do I most wish to become President”, but “which of Clinton or Trump would I most wish – or perhaps least not wish – to become President?”

If you’ve taken the effort to make it to the polling booth, your logical choice is to vote for one of the leading contenders, unless you think they’re both equally bad (or equally good) and someone else is better. That’s not their fault, nor yours – it’s the fault of the way votes are counted and converted into a result. It’s the fault of the “voting system”.

A voting system is simply a way to account for all the voters’ preferences, and pick a winner. In the US, the winner in each county is the one who gets more votes than any other. It’s a really simple system, and sounds fair. However, it means first of all that you can’t really express a preference for a less popular candidate without effectively throwing away your vote. This makes it very hard for smaller parties to get support, which in turn ensures they remain smaller parties.

It’s a chicken-and-egg problem: nobody will vote for a candidate that nobody’s voting for.

It also means, for example, that many candidates won’t even run. Bernie Sanders and Ted Cruz would love to be on the ticket right now; however, doing so would have guaranteed the defeat of their respective parties’ nominees; If Sanders was running but Cruz was not, Trump would win the election in a landslide, as Sanders and Clinton split the left-leaning vote. Contrariwise, if Cruz was running and Sanders stayed out, Trump and Cruz would both be obliterated in the polls, leaving Clinton with a record-breaking win.

If both Cruz and Sanders were running, as well as Clinton and Trump, well …  let’s just say – I’d pay to watch that.

So, the simple way used in US Presidential elections has some very perverse effects. You end up with two major candidates. Anyone else running has no real chance, and anyone else with a real chance doesn’t run.

There are other ways to count votes. One such was is called Preferential Voting, or Single Transferable Vote. There, a vote for a losing candidate gets transferred to the voter’s “Second preference”. Here’s an awesome explanation of how Single Transferable Vote works in Australia. This method is less widely used around the world than First Past The Post, but it’s been shown to be the “least bad” of all the methods where voters choose candidates by ranking them somehow.

Why do I say “least bad?”

It turns out, amazingly, that if voters choose candidates only by ranking them, there’s actually no “good” way to pick a winner. Really!

Kenneth Arrow was born in 1921, and studied mathematics, finally proving a very strange theorem about voting systems in his PhD thesis.

He proved that as long as you insist that:

If every voter prefers X over Y, then X will beat Y.

If X is beating Y, and nobody changes their preference between X and Y, then X will still be beating Y.

then there must be a single voter whose vote completely determines the outcome of the election. One person, one vote, just like North Korea.

If you’re in the mood for a deeper dive into political math, check out my write-up of Arrow’s Theorem.

And remember to go and vote on Tuesday if not before, either in the election, or in my little unscientific survey. Thanks!

Credits: Clinton and Trump Caricatures by Flickr user Donkeyhotey