Voting isn’t fair

If you’ve spent any time talking about American politics recently, you’ve probably heard about how the electoral college gives priority to certain voters or how some states make it harder for some people to vote than others. You may have even signed a petition promoting a national popular vote or rallied to enfranchise citizens who have been traditionally not allowed to vote. The idea that voting isn’t exactly fair is probably not surprising. What might be surprising is that, no matter how hard we try, we can’t actually design a voting system that is fair.

This block I am enrolled in MA110 – The Mathematics of Social Choice. This class focuses on how groups of people make decisions. The first week of the class, we examined a variety of different voting systems (which is a fancy way of saying ways to take people’s preferences and decide who wins an election). What we found out through exploration of these systems is that for elections with more than two candidates, no voting system is truly fair.

So what do I mean by fair? Before I list the criteria that we outlined in this class, I suggest taking a couple minutes to think about what you think a fair voting system might look like….. Okay, got your list? Now let’s compare.

Here are some of the things we decided should be fulfilled by a fair voting system:

  • Voters should be allowed to rank their preferences for candidates however they’d like
  • Every voter’s vote should be worth the same amount
  • Every candidate should be treated the same
  • Getting more votes should never hurt a candidate
  • If a majority of voters like a candidate the most they should win
  • If everyone likes one candidate more than another, the candidate that is less liked shouldn’t be able to win
  • If a candidate would lose an election, removing them as a candidate shouldn’t change who wins

How does this list stack up to your list? Did we come up with any criteria that you hadn’t thought of or do you have any you want to add to our list? Hopefully, you’ll agree that these are some important things to have in a voting system. Here’s the thing though – there doesn’t exist a single voting system (no matter how hard you try) that will satisfy all of these criteria at the same time. There’s a whole Theorem (called Arrow’s Theorem) that proves why this is the case. Ironically, one of the systems that is closest to meeting these criteria is a dictatorship! (It only violates the ideal that every vote should matter the same.)

At this point, maybe you’re resolved that it might be okay to drop one or two of these criteria (though not the one that lets it be a dictatorship!). If you’re okay with that, then I do have some solutions for you! Check back for a later blog post with some ideas for voting systems that seem okay.

Bridget

Hi! My name is Bridget and I am a third year from Denver, CO majoring in Mathematical Economics. I'm interested in the intersections of disciplines - especially how math connects to other parts of life - which often drives the academic circles I find myself in. I also really enjoy spaces where I get to share what I have learned with others (so yay blogging :)!).