Imagine we want to build a new space port at one of four recently settled  Martian bases, and are holding a vote  to determine its location. Of the hundred colonists on Mars,  42 live on West Base, 26 on North Base, 15 on South Base, and 17 on East Base. For our purposes, let’s assume  that everyone prefers the space port to be as close to their base as possible,  and will vote accordingly. What is the fairest way  to conduct that vote? The most straightforward solution  would be to just let each individual cast a single ballot, and choose  the location with the most votes. This is known as plurality voting,  or "first past the post." In this case, West Base wins easily, since it has more residents  than any other. And yet, most colonists would consider  this the worst result, given how far it is from everyone else. So is plurality vote  really the fairest method? What if we tried a system  like instant runoff voting, which accounts for the full range  of people’s preferences rather than just their top choices? Here’s how it would work. First, voters rank  each of the options from 1 to 4, and we compare their top picks. South receives the fewest votes  for first place, so it’s eliminated. Its 15 votes get allocated  to those voters’ second choice— East Base— giving it a total of 32. We then compare top preferences  and cut the last place option again. This time North Base is eliminated. Its residents’ second choice  would’ve been South Base, but since that’s already gone, the votes go to their third choice. That gives East 58 votes over West’s 42,  making it the winner. But this doesn’t seem fair either. Not only did East start out  in second-to-last place, but a majority ranked it among  their two least preferred options. Instead of using rankings, we could try  voting in multiple rounds, with the top two winners  proceeding to a separate runoff. Normally, this would mean West and North  winning the first round, and North winning the second. But the residents of East Base realize that while they don’t have  the votes to win, they can still skew the results  in their favor. In the first round, they vote  for South Base instead of their own, successfully keeping North  from advancing. Thanks to this "tactical voting" by East Base residents, South wins the second round easily, despite being the least populated. Can a system be called fair and good  if it incentivizes lying about your preferences? Maybe what we need to do  is let voters express a preference in every possible head-to-head matchup. This is known as the Condorcet method. Consider one matchup:  West versus North. All 100 colonists vote on their preference between the two. So that's West's 42 versus  the 58 from North, South, and East, who would all prefer North. Now do the same  for the other five matchups. The victor will be whichever base  wins the most times. Here, North wins three  and South wins two. These are indeed the two  most central locations, and North has the advantage of not being  anyone’s least preferred choice. So does that make the Condorcet method  an ideal voting system in general? Not necessarily. Consider an election  with three candidates. If voters prefer A over B, and B over C,  but prefer C over A, this method fails to select a winner. Over the decades, researchers  and statisticians have come up with dozens of intricate ways  of conducting and counting votes, and some have even been  put into practice. But whichever one you choose, it's possible to imagine it delivering  an unfair result. It turns out that our intuitive concept  of fairness actually contains a number of assumptions  that may contradict each other. It doesn’t seem fair for some voters  to have more influence than others. But nor does it seem fair to simply  ignore minority preferences, or encourage people to game the system. In fact, mathematical proofs  have shown that for any election with more than two options, it’s impossible to design a voting system  that doesn’t violate at least some theoretically desirable criteria. So while we often think of democracy  as a simple matter of counting votes, it’s also worth considering who benefits from the different ways of counting them.