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Imagine we want to build a new space port

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at one of four recently settled 
Martian bases,

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and are holding a vote 
to determine its location.

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Of the hundred colonists on Mars, 
42 live on West Base, 26 on North Base,

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15 on South Base, and 17 on East Base.

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For our purposes, let’s assume 
that everyone prefers the space port

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to be as close to their base as possible, 
and will vote accordingly.

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What is the fairest way 
to conduct that vote?

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The most straightforward solution 
would be to just let each individual

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cast a single ballot, and choose 
the location with the most votes.

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This is known as plurality voting, 
or "first past the post."

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In this case, West Base wins easily,

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since it has more residents 
than any other.

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And yet, most colonists would consider 
this the worst result,

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given how far it is from everyone else.

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So is plurality vote 
really the fairest method?

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What if we tried a system 
like instant runoff voting,

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which accounts for the full range 
of people’s preferences

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rather than just their top choices?

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Here’s how it would work.

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First, voters rank 
each of the options from 1 to 4,

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and we compare their top picks.

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South receives the fewest votes 
for first place, so it’s eliminated.

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Its 15 votes get allocated 
to those voters’ second choice—

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East Base— giving it a total of 32.

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We then compare top preferences 
and cut the last place option again.

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This time North Base is eliminated.

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Its residents’ second choice 
would’ve been South Base,

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but since that’s already gone,
the votes go to their third choice.

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That gives East 58 votes over West’s 42, 
making it the winner.

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But this doesn’t seem fair either.

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Not only did East start out 
in second-to-last place,

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but a majority ranked it among 
their two least preferred options.

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Instead of using rankings, we could try 
voting in multiple rounds,

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with the top two winners 
proceeding to a separate runoff.

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Normally, this would mean West and North 
winning the first round,

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and North winning the second.

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But the residents of East Base realize

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that while they don’t have 
the votes to win,

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they can still skew the results 
in their favor.

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In the first round, they vote 
for South Base instead of their own,

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successfully keeping North 
from advancing.

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Thanks to this "tactical voting"
by East Base residents,

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South wins the second round easily,
despite being the least populated.

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Can a system be called fair and good 
if it incentivizes lying

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about your preferences?

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Maybe what we need to do 
is let voters express a preference

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in every possible head-to-head matchup.

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This is known as the Condorcet method.

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Consider one matchup: 
West versus North.

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All 100 colonists vote on their preference
between the two.

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So that's West's 42 versus 
the 58 from North, South, and East,

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who would all prefer North.

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Now do the same 
for the other five matchups.

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The victor will be whichever base 
wins the most times.

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Here, North wins three 
and South wins two.

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These are indeed the two 
most central locations,

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and North has the advantage of not being 
anyone’s least preferred choice.

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So does that make the Condorcet method 
an ideal voting system in general?

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Not necessarily.

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Consider an election 
with three candidates.

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If voters prefer A over B, and B over C, 
but prefer C over A,

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this method fails to select a winner.

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Over the decades, researchers 
and statisticians have come up with

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dozens of intricate ways 
of conducting and counting votes,

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and some have even been 
put into practice.

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But whichever one you choose,

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it's possible to imagine it delivering 
an unfair result.

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It turns out that our intuitive concept 
of fairness

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actually contains a number of assumptions 
that may contradict each other.

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It doesn’t seem fair for some voters 
to have more influence than others.

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But nor does it seem fair to simply 
ignore minority preferences,

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or encourage people to game the system.

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In fact, mathematical proofs 
have shown that for any election

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with more than two options,

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it’s impossible to design a voting system 
that doesn’t violate

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at least some theoretically
desirable criteria.

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So while we often think of democracy 
as a simple matter of counting votes,

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it’s also worth considering who benefits
from the different ways of counting them.