How Losers Win. When First Past the Post Elects the LEAST Popular Candidate. It's worse than you realised.

I have in the past brought up the fact that first past the post voting can elect the least popular candidate, and even though I was talking in a forum with people in favour of electoral reform, I was told "that's not true".
It's not that they continued to assert that to be the case, it's just that they intuitively assumed this could not be the case until it was explained how it could be.
It is something that is objectively true and it's something provable mathematically.

Unfortunately, there are people who, despite being in favour of other forms of single-winner elections, still see FPtP voting as at least an adequate and legitimate way of holding an election.

First off, let's look at what you're trying to achieve in an election, you're trying to find the most popular candidate. Most popular amongst who, all of the electorate, right?
First past the post often does elect that candidate, however, it can also fail to do that. Although much less likely, AV can also fail to do that, what AV can't do is elect the least popular candidate.

Under FPtP, it doesn't matter how many people vote against you, what matters is how fragmented the opposition is.
If the opposition is highly fragmented, someone can win with very little support, and the winner can be the candidate who would not just lose, but lose badly against most other candidates, or worse, every other candidate.
The plurality metric for deciding a "winner" can in some cases be quite arbitrary.
Still, "most votes wins" can seem so highly intuitive that it would be fair, some people will immediately resort to Bulverism at the mere suggestion it's not, purely out of instinct.
Perhaps the worst thing about it isn't just that it can elect the least popular candidate, more the fact that the system itself seems so intuitive, trying to disparage it can get that reaction.

Put simply, first past the post voting can elect the candidate that would lose a two-person run-off against every single other candidate, this is also known as the Condorcet loser.
This is why I think it is one of the worst methods possible for elections that require a single winner where more than 2 candidates running.
I also find it odd that many countries that have PR such as New Zealand and Germany still rely on this system for their single-winner constituencies.
I think that may be down to how intuitive the system seems at first glance.

Someone could argue that what I described is not an adequate metric for deciding who is the least popular candidate.
Fair enough, if losing in a run-off to every other candidate doesn't make you the least popular candidate, I'd like to know what does?
However, even if I accepted that to be the case, I'd like to see how it could be argued that a person who would lose so consistently this way could still be deemed to be the most popular candidate? 🤔

How can this can happen?

Here is a simple example, If you run an election Tiger vs Bear and Tiger wins 60-40.

However, we run the election again this time it's Tiger vs Bear vs Monkey, and this time Bear wins. 35-37-28.

Just by deciding to run monkey has altered the result of the election just by running.

For clarity, we run the election again Bear vs Monkey and Monkey wins 45-55.
So, in a two-person run-off Bear would lose to either Monkey or Tiger individually. However, plurality voting allows Bear to win despite being overall the least popular candidate.

What's worse is that Monkey has inadvertently hurt his own voters.
Just by running, and encouraging people to vote for him, he's helped elect the candidate his supporters most disagree with.
 

This example may not seem too troubling. After all, some of the voters who had voted for Tiger did switch to Bear in the Monkey vs bear run-off. Obviously, Bear does have a high level of support and is likely not actively despised by those not voting for him, but he is still the Condorcet loser. 

What is troubling about it is, with only three candidates running, how likely this is to happen.

It can be a lot worse.

What if there was a First Past the Post election and there were many more candidates and worse people voting have little clue as to how other people are likely to vote and who has the best chance of winning?

This can be the reality for voting in elections for positions in many organisations, trade unions or local council elections.

With elections within organisations there can be many candidates and voters will have no idea before they vote who is likely to win, so with 9 candidates running in theory if there is a close to even split between candidates someone could win with 12% of the vote.

OK, that's highly unlikely to happen, but with voters having no polling to look at to know who is likely to win the vote has a high chance of being highly fragmented, it wouldn't be unusual for someone to with just 20% of the vote meaning 80% voted for someone else.

The Mixenden council By-Election of 2003 is almost certainly an example of the least popular candidate winning. It turns out Redmond Mellett was an anti-fascist campaigner who, just by running, inadvertently helped the fascist to get elected.

Admittedly, even for a winner with 20% of the vote, there is still a good chance that person would genuinely be the most popular and still go on to win in any kind of ranked choice voting system. However, there is also a good chance that could be a candidate who is seen as the worse possible candidate by most of that other 80% of the voters.

A good example of this in practice was the 2002 French presidential election.

Even under FPtP Jacques Chirac would have won that election. However, with a result so close and so fragmented it shows how close Le Pen got to winning the plurality of votes. Let's say he did, and there was no second round, how fair of a result would that have been for the majority of French people given what we know about what happened in the second round?

In the first round Chirac and Le Pen went through on 20% and 17%, which also means only 37% of voters voted for either of the top two candidates.
This is also an example of why just having just a two-round system isn't sufficient and why full Instant run-off voting is fairer.
I'll stick my neck out and state that La Pen would not have made it to the last round under such a system.

However, what this election and its second round did show is just how close plurality voting can come to electing the very worst candidate, especially when you see the result of the second round.

Some people in that second round would again be voting for their genuine first preference, and some people were ironically sanitising their feet outside the election booths at the thought of having to vote for Chirac. Yes, that actually happened. None of that matters, if you're voting for someone who was originally your first or 10th preference in the first round. Out of the two candidates remaining everyone was voting for their first preference.

The most important point to remember as to why ranked-choice voting is fair is because your vote does not and should not get to count more based on how emphatic you are about the candidate you're voting for.
You simply eliminate candidates who can't win so that their presence on the ballot cannot alter the result.

The Second round of that election showed how unpopular Le Pen was amongst almost everyone who did not emphatically want him to win in the first place. Chirac increased his vote by 62% to 82%  while Le Pen increase his vote share by a grand total of 1% to 18%.

This just shows how close plurality voting can come to potentially electing, not just an unpopular candidate, but the candidate thought of as the worst possible option by the overwhelming majority of the electorate.

This is just one of the reasons why the first past the post system is fundamentally flawed and unfair.