Gaming 3 party elections

This proposal on the upcoming federal election talks about some interesting gaming of the voting system.

In Canada, there are 3 (and sometimes more) strong parties. This is true in much of the world; in fact the two-party USA is somewhat unusual. However, with “plurality” style elections, where the candidate with the most votes takes the seat even though they might have well under a majority, you can get a serious difference between the popular vote and the composition of the house. Americans see the same in their Electoral college and in gerrymandered districts.

The author, who wishes to defeat the incumbent Conservative party, proposes a way for the other two parties (Liberals and New Democrats) to join forces and avoid vote splitting. The Liberals and NDP are competitors, but have much more affinity for one another than they do for the Conservatives. They are both left-of-centre. This collaboration could be done at a national party level or at the grass roots level, though it would be much harder there.

Often in parliaments, you not only get splitting within the race for each seat, you get a house where no party has a majority. For minority governments, one party — usually the largest — strikes a deal with another party for a coalition that allows them to govern. Sometimes the coalition involves bitter enemies. They cooperate because the small party gets some concessions, and some of their agenda is passed into law, even though far more of the dominant party’s agenda gets passed. Otherwise, the small party knows it will get nothing.

The proposal suggests two parties should collaborate before the election, rather than after. It identifies 16 ridings (what in the US would be called districts) where the Conservatives have a slim lead over one of the left parties, and the other left party is well behind. The argument can be made that, even with the unreliability of polls, it’s very clear that the 3rd place candidate is not taking that seat. They propose that this 3rd place candidate publicly throw support to the other left candidate. (It’s too late to physically withdraw.) If done, this would work, and 8 candidates from each left party would be elected instead of 16 Conservatives, and that should indeed swing the election if other polls are right.

On the surface, that seems very rational. Polls are notoriously wrong, particularly in parliamentary elections, but they are getting better and there is a limit to their error. Candidates can indeed know they are not going to win, and they are fighting just on principle. They can know that by fighting, they will split the vote and give the riding to the Conservative. Again, the NDP and Liberals are far from tight bedfellows, but they both see the Conservatives as their main opposition.

Even in spite of the numbers, this can still be a lot to ask somebody who has put so much into fighting a race. They would be asked to “take one for the team.”

For the parties, the rationality is much more clear. The main negative would be that some would see this as cheating, though it is the norm in all leadership conferences to have the winner decided by losers who throw their support when they can no longer survive. There is also the slight risk that serious poll errors could result in a candidate withdrawing who later is revealed to have had a chance.

The parties could go further. With the chance to be the government, they could offer perks and rewards to the candidates who withdraw to take one for the team. All the way up to safe seats in future elections, or seats in the Senate, though it would be hard to reward all them that way. They would need to be stars in the rough — you don’t offer perks like that to people who are losing for a reason.

What all of this would do is reduce vote splitting. The real way to do that is to switch to some sort of multi-candidate election. That’s an election where instead of just picking one candidate on the ballot, you can name 2 or more, and possibly rank them in order. In Australia, this is how elections are done. The ordered ballots allow the lowest candidate to be eliminated and an instant runoff done with their votes distributed to their supporter’s second choices, and so on until you have only 2.

The Australian STV system is well tested, but it has a number of flaws and confuses voters a lot. Today, many election theorists like some other systems. The Condorcet method is good if you have a rank ordering, though it sometimes generates 3-way ties. I have come to favour the vastly simpler Approval voting system, where you can simply vote for as many candidates as you like — with no ranking. It has some slight strategy to it (unlike the ranked ones) but is super easy to understand and use, which turns out to be important. The public has to understand the system and have faith in it.

Why don’t we use these systems today

Some countries do use them, but most don’t. One reason it’s hard to switch is that there are always powerful entities who would suffer if a switch were made to the counting system. That’s true for any switch — in fact, we would not seek a switch if it would have no effect. Not only that, most parties can see that while sometimes the new system would help them, in other times it would hurt them. They don’t like the risk.

If changes require constitutional amendment — and in many countries, they do — it becomes almost impossible to pass something that has super strong opposition from powerful parties. In the USA, it’s clear that such systems would have altered the 2000 Florida results strongly for Gore, but they would also possibly have altered the 1992 election over from Clinton to GHW Bush with the Ross Perot factor eliminated. Neither party is going to get strong support behind that trade-off, and as such it is hard to make it happen.

In Canada, a change to federal election rules might be possible just in the Elections Act, not in the constitution. So if a coalition that was very strong decided to gain power with this trick, and then put it into the law, it’s not out of the question.

Politics, however, is about people sometimes even more than principle. Asking people to step down like this is a pretty big step. So I doubt it will happen.

PR

No, not public relations, but proportional representation. Even with schemes such as STV, instant runoff, and the others you mention, there is still the concept of candidate for district. Get rid of that! Most people don't know the candidates personally anyway, and people at least should vote for ideas. It is a stretch even applying the word "democracy" to non-PR systems.

For those who can't divorce themselves from the concept of a representative for a district, adopt the German system. The parliament is elected with PR. In addition, there are "direct candidates" for each district. However, these count toward the number of seats which the corresponding party has. (If a party has more direct candidates who win then the number of seats they should have, the size of parliament is increased accordingly.)

One step at a time

That’s a radical change. Radical change may be the right step but it’s hard to get people to adopt it because it would shift the political system so much the parties would not know quite what to do.

Actually, there are candidates who are quite well known and loved in their ridings, but of course many are fairly unknown as you say.

There are all sorts of even more interesting things than proportional representation to try.

And then there is the reason for districts and representatives. Most nations are not unified, homogeneous blobs. They tend to consist of regions which have their own politics and character. These systems demand that a party get support all over the country in order to hold power, while in proportional representation, a party might hold all its strength on one side of the country, and have barely any on the other side, but as long as it’s the largest party or 51% party, it wins. Most countries want to stop that — and indeed, when they were formed, they agreed to things like the US Senate as the condition on which they would join, because it discourages that.

Maybe, but is that bad?

"That’s a radical change. Radical change may be the right step but it’s hard to get people to adopt it because it would shift the political system so much the parties would not know quite what to do."

That might actually be a good thing. Of course, parties wouldn't want to saw of the branch they are sitting on, so of course it will be hard to implement.

Radical? Well, many countries have been using it for decades. It's not that radical (although in the States I'm sure some Republicans would say that it is a form of communism).

"Actually, there are candidates who are quite well known and loved in their ridings, but of course many are fairly unknown as you say."

They might be well known, but usually voters don't know them personally. The whole idea of voting for a person is usually not the best way to do things, except in situations where most voters do know at least their candidate personally.

"There are all sorts of even more interesting things than proportional representation to try."

Sure, from a game-theory point of view, but how can one improve on "x per cent of the votes, x per cent of the seats"?

"And then there is the reason for districts and representatives. Most nations are not unified, homogeneous blobs. They tend to consist of regions which have their own politics and character. These systems demand that a party get support all over the country in order to hold power, while in proportional representation, a party might hold all its strength on one side of the country, and have barely any on the other side, but as long as it’s the largest party or 51% party, it wins. Most countries want to stop that — and indeed, when they were formed, they agreed to things like the US Senate as the condition on which they would join, because it discourages that."

What you say might be more credible if there were some objective way to draw district lines, as opposed to gerrymandering. For example, imagine a city with 2/3 whites on one side and 1/3 blacks on the other. Assuming that people vote for their race, or for a candidate which they feel best represents the interest of their race (this is just an example, but not completely unrealistic), surely 1/3 of the representatives should be black. But what if the district lines are drawn so that each district is 2/3 white?

I think this is a red herring, though. In a national election, what matters is the national percentage. Local politics should be handled at a local level. Handling it at a national level leads to pork-barrel politics.

The idea that "it wins" if it is the largest party, even if less than 50 per cent, is not correct. In most cases, there would need to be a coalition. There could be a minority government, with shifting majorities on individual policies (not necessarily a bad thing), but of course tolerated by the opposition.

Gerrymandering

Is, I hope, and unintended consequence of having districts. They just did not realize that if they let the states draw the lines in meant parties would draw the lines to cement power.

Having geographic representation however was not unintended. In fact, in the formation of many nations, it was the only option. Many nations were formed either by adding regions one at a time to a whole (like the USA) or by a group of regions coming together and deciding to be a country. But any given region (especially a new region) is going to say, “Hey, we can join your country, but since we are only going to be 5% of it, we won’t be represented directly in the ruling group, so we insist that we be guaranteed that 5% (or even more) of the members of the governing entity come from here.” They won’t join if they don’t get that — and later, you get the bad results. It seems like a good idea at the time. Sometimes it is even still a good idea today.

The US electoral college, while decried in the rare times it means the winner did not win the popular vote, was intended to do that. The founders fo the USA wanted to make sure that a candidate with super-high local popularity in one region and only modest popularity in the rest of the country could not win, even if they got most of the popular vote. That this would be too divisive, and you would not want it to be able to happen to you.

No easy answers

One of the most discouraging results in the dismal science of economics is "Arrow's impossibility theorem" which proves that there's no way to create a voting system that is always fair or stable in a 3-party system. I wouldn't recommend the American 2-party system to anyone, but at least it's simple.

Sort of

You can’t have a stable system if you want to have only one winner. Rarely considered is the option that if the system has an unstable result, you have a tie, and you must resolve it another way. The tie is going to be quite rare. In Condercet it’s a 3 or more-way tie, with even 3 being quite rare, but in that event the public really didn’t know what they wanted and so the error is assuming that one of those 3 candidates is the “right” choice. In fact, none is, and so it’s time for a different system or election, or even dice, or best of all, co-government. Because in that situation you should have co-government. With 3 that’s actually pretty easy, as all votes are quickly resolved. 4 way should be so rare I am not bothered solving it with random chance eliminating one of them.

So?

"no way to create a voting system that is always fair or stable in a 3-party system"

So don't use a three-party system.

People spend a huge amount of time thinking about how to slightly perfect essentially bad systems. Much better would be to go to a much better system.

Not use a 3 party system

I don’t know of anywhere that has a 3 party system. What they have is a generalized multi-party system (or parties may not even technically exist in the rules) and 3 parties of note have formed (there are usually several minor parties too.) Even the 2-party systems like the USA are not officially 2 party systems.

So how do you “not have a 3 party system?” You can not have parties, in that you don’t give parties any specific existence in the system, but that’s already the case in many countries. If there is an advantage to be had by joining together into parties, people will do it, and it’s pretty hard to ban. Even direct democracy systems end up with parties, people who get together and trade votes because it gets them more than those who don’t. It’s harder in a secret ballot, but far from impossible, and it happens.

Even simpler

" I wouldn't recommend the American 2-party system to anyone, but at least it's simple."

Even simpler is the one-party system.

Fixing the self-interest problem

To fix the problem of not being able to pass changes to election laws, we could schedule the change to take place 20 years into the future or so. That way the current parties will be less sure whether the change will be good or bad for them and so might consider it more on it's merits.

This same principle could help with other problems like gerrymandering too.

Still difficult

We can’t predict the future, so we’re often more scared of that.

The victors in US gerrymandering are Republican house members. How would yo convince Republican governed states that it is to the advantage of their party to eliminate this gerrymandering in 20 years. (That’s not very long, it’s only redrawn every 10 years anyway.)

Those in power have no motive to shake up the system unless they are convinced the shakeup will strengthen their power.

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