Approval voting and primaries

California and Washington both use the top-two, open primary method in their elections: voters get to pick from, regardless of party, any primary contender to go onto the general election. The top two vote getters in the primary, regardless of party, move on to the general. One consequence of this is that a party could get "locked out" of a particular race if none of its candidates qualify for the top two spots. As a result, the parties have been especially concerned with having too many candidates in a race and splitting its voters into too-small factions, thus depriving any of the party's candidates from making it onto the general ballot. See this article for a description of the problem.

There's a very easy, very simple fix for the second part of this problem: approval voting. Here's my two-sentence description of approval voting:

Each voter can put a check next to as many candidates as they approve of, leaving disapproved-of candidates blank. The candidate(s) with the most votes win(s).

That's it. Ballots look the same. It's not complicated to explain. And approval voting lends itself to virtually no strategic voting (i.e., faking your preferences on the ballot to try to induce your desired outcome to happen).

In the top-two primary, everything would work the same, except that voters wouldn't get one choice; they could vote for as many candidates as they like. ABBAs could vote for every ABBA candidate, and BeeGees could vote for every BeeGee candidate. Or ABBAs could vote for most ABBA candidates and some centrist BeeGees. Or a centrist could vote for some centrist ABBAs and some centrist BeeGees. Let's imagine a scenario in which a district is 51% ABBA voter and 49% BeeGees. Let's say each side nominates three candidates: A, B, and C for the ABBAs, and X, Y, and Z for the BeeGees.

In a hyper-partisan environment, 100% of ABBA voters approve of A, B, and C, and 0% approve of X, Y, and Z; vice versa for all the BeeGee voters. Because there are slightly more ABBA voters (51-to-49), therefore the top two candidates will always be some combination of A, B, and C (more on this in a second). The BeeGee would be locked out. However, this lock-out has nothing to do with how many candidates the BeeGees nominated. It would have happened whether they nominated two, three, four, or a hundred candidates. The lock-out is the result of the hyper-partisan environment, not the number of candidates nominated splitting the vote. No matter how many candidates the BeeGees nominate, they all get 49% of the vote and fall short of the general ballot.

Let's go back to that issue of which two of A, B, and C make the general ballot in the hyper-partisan environment. If it is truly a tie--all three got exactly the same number of votes--then some tie-breaking mechanism would have to be employed. They could draw straws, or the ABBA party chairperson could decide because all of the candidates are its own. But this three-way tie seems fairly unlikely. Would primary ABBA voters be so united in support of all three candidates that they give 100% approval to each? I guess this is an argument that such hyper-partisanship seems unlikely; it's more likely A gets 95% approval from ABBA voters, B gets 90%, and C gets 70% or some such split. If there aren't at least two of ABBA's candidates that get 100% approval from ABBA voters, it opens up the possibility that a BeeGees candidate can make it to the general election.

Furthermore, it seems unlikely that there are no unaffiliated voters exist and that none of the partisans ever cross-over. Even in today's highly partisan environment, people can and do split tickets, switch parties, and cross-over. (I reserve hyper-partisanship to mean zero behavior exists.) Some ABBA voters might approve of A, B, and Z. Some centrist voters might approve of B and X. Having unaffiliated voters and cross-over votes doesn't guarantee ABBA candidates or BeeGee candidates won't be locked out--but it does make it less likely. Even in a highly partisan environment, candidates with cross-over appeal might be at somewhat of a practical advantage. Winning 99% of 51% of the total votes (almost all ABBA voters) is 50.49% of the total; winning 90% of 51% of the total votes (most ABBA voters) and 10% of 49% of the total votes (a smattering of BeeGee voters) is 50.8% of the total votes. As a real-world matter, I think it's harder to get complete party unity behind a candidate (that is, 99%) than it is to attract a couple percentage points from the other party. Maybe I'm wrong, but look at this graph of presidential approval ratings. Of the twelve presidents of the modern era, nine were able to pick up more support from the opposition party than they lost from their own. Only two were better able at holding their own party together than at attracting opponents (Barack and the Donald). The twelfth case, Jimmy, did dismally with both parties. The average trend is that pulling in opposition is easier than preventing any defections.

In an approval voting scheme for a top-two primary, it's possible that a party gets locked out, but the cause would not be how few or many candidates they nominate. A party would get locked out if (1) the other party had more voters and had at least two candidates they completely unified behind or if (2) the other party had at least two candidates with cross-over appeal. Scenario 1 seems unlikely as an empirical matter; scenario 2 seems like it fulfills the exact purpose of top-two primaries of selecting the two best candidates overall--who just happen to be from the same party, but expanded their support beyond it.

By the way, the approval voting scheme makes sense for regular primaries too, or any time voters have more than two choices they need to whittle down. I use it in meetings whenever we have more than two options to consider to find out where the general consensus lays.

There's not much an individual voter can do to vote strategically. Some might consider giving an approval vote to the candidate I find least objectionable from the party I disagree with, if I think it's inevitable that the other party will get one candidate in. (In other words, it's inevitable, so chose the weakest opposition.) This seems an unlikely scenario, however, and a risky strategy. When do I know the other party is nearly guaranteed a spot in the general election? Only when my party has nominated only one candidate or only one strong candidate (so, unlikely). And it's a risky strategy: my approval vote for the weakest opposition might be enough to push TWO of the opposition party's candidates into the general election, excluding my candidate entirely. Let's say the standings look like this, including my vote for my candidate but not yet voting for the opposition candidate:

My candidate - 51%
Opposition candidate I hate - 49%
Opposition candidate I would prefer - 49%

In this case, I do get to decide which opposition candidate we face in the general election. But the scenario could just as easily be this:

My candidate - 49%
Opposition candidate I hate - 51%
Opposition candidate I would prefer - 49%

In this case, the opposition candidate I hate is inevitable. My vote for the opposition candidate I prefer knocks out my candidate. (At least before, my candidate might have won the tie-breaker for second place.)

Who can say which scenario is likely to happen in a close race before the voting is done? This strategy is incredibly risky when everyone votes before votes are tallied.

Proportional representation 2

I write this with trepidation, since I think people invest a lot in their own preferred voting schemes. But I believe I have a novel proportional representation voting method, so I'd like to share it whether it is good or not. I have not encountered an approval voting method for multi-seat elections, so here goes.

Let's say there are three seats in a district. Let's also say there are three parties, each nominating three candidates, for a total of nine. Each voter chooses his top three candidates (because there are three seats). The voter may vote straight down a party line, or he may pick and choose from the different parties. The results are tallied like so.

1. All possible three candidate combinations are listed.
2. For each combination, each voter's ballot is used to score it. If there is one candidate he approves of, it gets a score of 1 point from him. If two candidates, 1.5 points. If all three candidates, 1.75 points.
3. This is repeated for every voter's ballot for every possible combination (obviously, this must be done by computer).

This is somewhat like a jungle primary, except there is no runoff. (The top two system does seem intriguing.) Here is an example.

The columns headers show the sizes of voting blocks. Out of the 90 total voters, the biggest plurality, 35 voters, prefer Party 1. A block of 10 voters prefer candidates B, E, and H; a block of 5 voters prefer C, F, and I. Obviously, Party 1 deserves at least one seat, possibly two; Party 2 might deserve just one seat; and Party 3 might be below the threshold to get a seat at all. But which candidates from each party?

There are 84 possible combinations, so let's focus on the highest scoring combinations.

The "1 pt" column indicates what would happen if only the voter's first approval counted. The next column indicates the tally method I described above. Some comparisons are interesting: ABF is a higher-scoring combination than ABE -- sure, the block of 10 voters is happier having two candidates of whom they approve, B and E, but the ABF combination brings in a candidate whom the block of 5 voters like.

The ultimate winners are B, C, and E: two seats for Party 1, one seat for Party 2, and zero for Party 3. Now, before anyone says that this is unfair for this or that reason, just remember that no voting system is perfectly fair. Kenneth Arrow wrote about voting systems and proved that no system could simultaneously meet all three of his sensible criteria. Instead, let me just lay out some of my choices in creating this method.

Why did I choose approval voting? A: I think you open it up to a lot of strategic voting if you allow people to rank candidates -- people can choose to tinker with their votes down toward the bottom of their list to give their own preferred candidates at the top of their list the best chance of winning. I'm not sure that the same can be done with approval voting. Let's say I'm a hard-core partisan of Party 1. I know that realistically my party is likely to win one or two seats, but not three. I might be tempted to use my third vote to influence the candidate who gets chosen in Party 2 (thus voting, perhaps, ABD in the above scenario). But I have to realize that the voting method cannot tell that I dramatically prefer A or B to D. It makes the gamble riskier, I think.

Why did I choose only three votes? Short answer: Because there were three seats. Long answer: I think that this constraint forces people to think carefully, and my gut says it makes it even harder to vote strategically. As a variant system, I think it might be interesting to consider giving each voter (seats - 1) votes, so in this case, two approval votes. The reason would be to force each partisan voter to indicate which candidate in his own party he least likes. This actually puts more power into the party supporters', not the party leaders', hands.

Why did I choose the "first candidate approved of equals one point, while second candidate approved of equals 1.5 points?" A: The reason that I set up the point values that I did is so that it is worth more to get voter A one candidate whom he likes than to select for voter B the second candidate whom he likes. In this way, this voting method tries to get everyone one representative, before it tries to get anyone a second representative. The pattern would continue: 1, 1.5, 1.75, 1.875, 1.9375 . . .

I have not done the math to see what all the ways to strategically vote are, but my guess is that in the end, the smart "game play" for a party is to nominate candidates who can attract swing voters. In my scenario, the 15 total swing voters ended up deciding where the third seat went and also deciding which candidates got elected from each party. In the real world, perhaps this would mean that a multi-seat district could be representative (in the sense that most voters approve of at least one of their representatives) AND competitive (in that the swing voters always produce some fluctuation). The idea I'm most attracted to is that even a popular party's incumbent could be thrown out. In the above scenario, just assume for a second that candidate A and B are their party's incumbents. Perhaps A was involved in a scandal. Party 1 still might retain one or two seats [they have the block of voters to do it], but disgusted swing voters can make clear that candidate A must go.

I welcome any scenarios readers come up with to show weaknesses to strategic voting in this system. Please share them.

On an interesting note, ranked choice has the problem of complicating things too much for voters. Of course, in the article, the larger point is the critique that a desire to change elections is often actually motivated by a desire to change politics. But repressed interests won't always naturally bubble out. People might not spend the time to learn about the candidates. People might still vote in habitual, not considered ways.

This is a fair point. A new system of voting should be simple. Approval voting, with the option to vote down a party line, fits that bill. If one was really concerned about overvoting, one could drop the limit on how many candidates a voter could approve of; even if a voter approved of every candidate on the ballot, it would still be valid. Certainly, approval voting would have far fewer problems with incorrect ballots that ranked choice. And it doesn't require extensive knowledge of the candidates like range voting.

As to the other part of the critique, I do think proportional representation would actually change our politics. So I'm guilty of some optimism there. The reason is simple, though: proportional representation would probably create a 45-45-10 political system, where the numbers stand for Democrats-Republicans-Third parties. I think the Green Party, the Libertarian Party, and on and on would bring policies to the table that are missing. Nothing magical. Just a more open debate.

UPDATE, March 15, 2019: As my good friend Dr Paul Snell pointed out, my system definitely creates an opportunity for voters to vote strategically. A voter who wants to give their favored candidate the best possible chance should only vote for that candidate. That means there's only one way for the method to "score" a point for that voter, as opposed to someone who's voted for three different candidates. The latter voter's approval is more diffuse and the voter can be "satisfied" by more different outcomes. If everyone votes in this strategic fashion as the first voter--voting for only their top candidate--then the method reverts back to first-past-the-post.