Can you minimize wasted votes without electing Nazis?

You can, with a good rigorous definition of “wasted votes”.

Wasted votes are an important political problem.

No, I’m not talking about ballots trashed by fraud, like these Turkish ones, but about ballots trashed by the normal operation of the voting method.

That’s clear from many examples, especially in the 3 main Anglo-American countries. Here are just a few:

In the US, gerrymandering — the process of drawing district lines to weaponize wasted votes—has reached epidemic levels. Roy Moore lost the election for Senate in Alabama, but the state’s gerrymander was still clear from the fact that he won more votes in 6 of 7 House districts. Court cases in North Carolina, Wisconsin, and Pennsylvania still haven’t resolved allegedly unconstitutional partisan gerrymanders going back to 2011.

In Canada, the current government has a false majority — a majority of Parliament even though it got a minority of votes. Is that unusual? No; it’s the 14th time it’s happened in the last 100 years. That’s an average of every 7 years, or every 5.5 years over the last 50.

In the UK, the DUP got 1.5% of parliament with 0.9% of the vote, while the Greens got 0% of parliament with 1.6% of the vote. Similarly, the Liberal Democrats got more votes but fewer seats than the SNP. Something screwy is definitely happening.

And of course, I can’t write a politics article without mentioning Trump, who got 10 million fewer votes than his opponents, and 3 million fewer than specifically Clinton.

If there’s just two candidates and only one can win, a large number of wasted votes are inevitable; no election method in the world can guarantee fewer than 49%. Since these single-winner situations are what we tend to think about when we imagine elections, it’s tempting to become jaded about wasted votes. Majority rules, minority drools; isn’t that just the way it is?

But when you’re electing not just one winner — a president, governor, or mayor—but rather many at once—a legislative body—wasted votes are not necessary. Imagine that instead of 2 candidates for 1 seat, you have 10 candidates for 9 seats; intuitively, you can now guarantee not just fewer than 50% wasted votes, but fewer than 10%. That is to say, you can ensure that at least 90% prefer some candidate who won over the one who lost.

How do you extend this idea of “wasted votes” from a situation where there’s just one more candidate than there are seats, to one where there are any number of candidates? Ensuring that “at least 90% prefer some winner over some loser” would be easy, but nearly meaningless; just add one horrible candidate to the mix, and any other slate of winners would pass that test.

To reduce the multiwinner case to the single-winner case, you have to pick not just a set of winners, but also the “strongest” loser. Then, you can use the definition:

Wasted votes are those which prefer the “strongest” loser over all the winners.

In principle, it’s possible to ensure that wasted votes, under this definition, are less than 10% in the example above with 9 seats; or, more generally, less than V/(S+1), where V is the total number of votes and S is the number of seats. In voting theory, this is known as a “Droop quota”.

This kind of thinking quickly leads to the idea of proportional representation: voting methods that ensure that a group which makes up, say, 30% of the voters can get 30% of the representatives. Most importantly, prop-rep methods ensure that 45% of the voters can’t get 55% of the representatives, avoiding false majorities like the Canadian ones mentioned above.

To be truly proportional, a method not only needs to ensure that no losing candidate gets over a Droop quota, but also that every winning candidate does. That is to say, just because one of the winners has two Droop quotas of votes, doesn’t make it OK to give the next seat to your niece who has zero Droop quotas of votes. You have to take the excess votes from the first winner, and give them to somebody else those voters would like, not to your niece.

There are many proportional methods that can make this kind of guarantee, but perhaps the most intuitive one is Single Transferable Vote, STV. As the name suggests, this works by transferring votes. You find the winners by eliminating the weakest candidates and transferring votes until somebody reaches a Droop quota; you transfer any overvotes that winner has; and you keep going like that until all the seats are filled.

STV is a pretty good voting method; certainly, a whole lot better than “First Past the Post” (FPTP), the method we use in the Anglo-American countries. But it does have its flaws.

One of STV’s flaws is that it requires voters to evaluate and rank all the candidates; a burdensome task, even for some of the most-engaged voters. There’s two ways to lighten this burden. One way, common in countries that use STV today, is to restrict voters to 5-member districts; though this cuts them off from the freedom to vote outside the district, at least it means they only have to rank a more manageable number. But though this reduces the complexity of the ballot, voters can still have to rank over a dozen candidates.

The other way to reduce STV’s complexity is to use delegation, as in PLACE voting. This means that when you choose your favorite, you’re also implicitly letting them help you rank all the other candidates. In PLACE, the candidate only divides the others into four tiers: from closest to farthest these are “factional allies”, “same party”, “coalition allies”, and “other (enemies)”. Within each tier, ballots from other similar voters set the specific rank order.

But the other flaw of STV has more to do with the definition of a wasted vote. The problem is, if voters can rank all candidates freely, there is little incentive to band together into parties. Fringe candidates will win seats on single-issue campaigns, so that after the election when they have to build a majority coalition to pass some law, they’ll be starting from scratch, without a larger coherent platform or vision as to whom they should ally with. This post-election landscape will by hyper-attuned to specific interests but could well lose sight of the general interest.

Now, don’t get me wrong, I’m not saying fringe groups of voters can’t be right. I’m a fringe voter myself; if all my dearest-held policy views were turned into the platform of the Jameson party, I’m sure it would get a negligible number of votes. But it’s healthy for a voting method to push people to build coalitions before as well as after the voting happens, and it’s legitimate to keep the most narrow and divisive candidates from winning seats even if they have over a Droop quota of supporters.

In other words, even if the Nazis have 4% of the votes, they shouldn’t necessarily get 4% of the seats. I’m using “Nazis” here not literally, but as a stand-in for fringe groups in general; depending on the time and place, you might substitute “socialists”, “libertarians”, “atheists”, “Christians”, “Muslims”, or “Jews”. But remember, in order to be fringe, a group has to not just be a small minority, but also be seen by the large majority of other groups as enemies rather than as allies. If that marginalization is unjust, there’s nothing democracy can do to fix that; but it can at least give incentives for groups not to self-marginalize.

How does that square with the definition of wasted votes above? Imagine you’re electing 99 legislators, so the goal is to keep wasted votes under 1%, and you choose no Nazis. If a Nazi candidate were the “runner-up” you used to define wasted votes, then the 4% of Nazi votes would all be wasted—way over the limit. So does prop-rep mean that you have to elect Nazis?

Not if you make rules that the runner-up has to show some kind of broad support. For instance, in PLACE voting, no candidate can win unless they carry at least 25% of the votes from their local district/riding/constituency. That will (hopefully) keep truly fringe candidates and parties out, while still allowing smallish parties and/or independent candidates a chance. A party with as little as 10% nationally is likely to reach the 25% threshold in at least a few districts; one with even 20% nationally is likely to pass the threshold in over 20% of districts, and so get its true proportional share.

But even as you eliminate the most fringey candidates, it is still crucial not to waste those votes. Those votes must be transferred to the next-closest party, as they are in PLACE, and not simply ignored, as below-threshold votes are in Mixed Member Proportional (MMP) methods.