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.