Which voting system is the best? - Alex Gendler

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Imagine we want to build a new space port at one of four recently settled Martian bases, and are holding a vote to choose its location. Of the 100 colonists on Mars, 42 live on West Base, 26 on North Base, 15 on South Base, and 17 on East Base. Assuming that everyone wants the port to be closest to their home base, what is the fairest way to conduct the vote? Alex Gendler digs into voting systems.

Lesson by Alex Gendler, directed by Biljana Labovic.

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.