Can a change in the voting system save our country?

Start with a simple electoral model: two strong, instrumentally rational parties; one dimension of political discourse (a simple left-right axis); and a simple majority voting rule where each voter selects the party closest to his location on the axis. How do the two parties behave? It’s simple, they each adopt a position very close to the view held by the median voter.

If one party deviates from the 50th percentile view, it will earn fewer votes than the other one. Suppose one party tries to shade a bit right, running on a platform equivalent to the view of the 60th percentile voter. This party will win the 40 percent to its right, but it will lose the 50 percent of the vote to the left of the other party and some of the vote in the middle, ensuring a victory for its opponent.

Under the assumption of simple majority voting, the system is stable against new parties. If a new party emerged on the right, it would split the vote on the right side of the spectrum and the voters on the left side of the spectrum would be unified. Because a new party only strengthens its polar opposite party, two parties continue to dominate. Because both of the stable parties espouse views close to those of the median voter, no matter who wins, policymakers adopt policies favored by the median voter.

This state of affairs—two parties, a policy status quo that is generally centrist—actually exists in the United States. Consequently, the median voter theorem is often taken to be a good first approximation of American politics, despite that some of the assumptions are too strong (e.g., single-dimension issue space).

But actually, American politics have been changing, and a slight tweak to the model can help us see how. Let’s weaken the assumption that the parties are strong and instrumentally rational. Perhaps (and I’m just spitballing here) a technology like the Internet comes along that empowers activists at the extremes of each party. No matter the cause, assume that it becomes harder to maintain party discipline. For concreteness, let’s say party bosses lose control over who runs in primary elections.

Because parties select candidates through a primary vote, simple application of the median voter theorem in the primary dictates that the left party selects a candidate at the 25th percentile of viewpoint and the right party selects a candidate at the 75th percentile of viewpoint. If the most extreme voters are more likely to be engaged during primary season, it could be worse. If at least some voters are strategic and concerned about electability, it might not be so bad. The winning primary candidates might still moderate their views a bit in the general election, because the battle then is still for the centrist voters. But the bottom line is that we are no longer in an equilibrium where both parties run on a median-voter platform. There is now daylight between the parties, purely as a result of the parties becoming weaker.

This change in party strength doesn’t create any long-term policy victories. Sometimes the left wins, sometimes the right wins. No political victory is ever permanent. Long-run policy continues to be near the preferences of the median voter, but now we get there by ping-ponging back and forth between left administrations and right administrations. A culture war develops. Left and right start to hate each other. But from a policy perspective, it is all pointless—however painful the culture war, the median voter still wins on policy in the long run.

These two models are only models—the assumptions are unrealistic in some ways. And yet, they are illuminating. In both cases, the median voter theorem holds in the long run—the policy outcome remains near the 50th percentile of the distribution. But in the second model, the way we arrive at this policy equilibrium is much more unpleasant. When party discipline breaks down, we don’t converge on median voter preferences as quickly as we do with strong parties, and therefore the culture war escalates.

Wouldn’t it be nice if we could have stronger parties again? Elites within each party could select candidates in smoke-filled rooms once again, choosing them based not on how ideologically pure they are, but rather on how likely they are to win. Returning this instrumental rationality to party politics would indeed be welcome, but it seems unlikely. The genie is out of the bottle. Power has shifted. Party elites are no longer in charge.

If we want to rapidly converge on moderate policy platforms but we can’t have strong, disciplined parties, another approach is to change the voting system. The discussion above assumes a simple majority voting system, but that is not the only option. Some voting systems do not systematically disfavor third parties and could therefore increase competition between parties. We can converge quickly on a moderate position due to strength and discipline within parties, but or we can do it due to weakness and competition between parties.

Consider a race between a candidate on the far left candidate and one on the far right. Instead of a simple majority election, we allow voters to express preferences in rank-order format. With this format change, a moderate candidate can enter the race, and voters can support her without splitting the vote and making it more likely that their most disfavored candidate will win. There are many ways of tabulating rank-ordered ballots, and Arrow’s theorem says no voting system is perfect. But let’s first examine social preferences in pairwise form.

Because every voter ranks candidates in his or her preferred order, we are able to use ballot data to say who would win in a two-way race between any pair of candidates. In the race between far left and far right, when a third moderate candidate enters, the moderate candidate will be preferred by most voters to the far-right candidate, and the moderate voter will be preferred by most voters to the far-left candidate. When a candidate beats all others by pairwise comparison, the candidate is called the Condorcet winner, and a voting method that always selects as the victor the Condorcet winner if there is one is called a Condorcet voting method.

The advantage of a Condorcet method is that the Condorcet winner will always be a moderate close to the median voter. The disadvantage of a Condorcet method is that there isn’t always a Condorcet winner. Just as in rocks-paper-scissors there is no option that beats all the others, in a three-or-more-way race, no candidate may be socially preferred to all others. This can happen if the issue space is not one-dimensional as we have been assuming, or if voter preferences are not single-peaked. A Leninist, for example, may support either a far-left socialist or a far-right hypercapitalist more than a centrist candidate.

The possibility of such circular ambiguity requires a way to resolve it when it exists. There are dozens of proposals for how to do so. Often, they take the set of candidates to whom the ambiguity applies, known as the Smith set, and apply some secondary criterion. For example, one could conduct an instant-runoff election between these candidates. This is known as Smith/IRV.

Another interesting method, perhaps my current favorite, is applying approval voting to the Smith set. In addition to ranking candidates on their ballots, voters could draw a horizontal line on their ranked list. Above the line, they approve of the candidates; below, they disapprove. If the Smith set has more than one candidate in it, select the most-approved of these candidates. This method, called Smith/Approval, is attractive because approval voting itself tends to favor moderate candidates. This approach piles a moderate-favoring method on top of another moderate-favoring method.

Other voting methods don’t try to find a Condorcet winner and instead go with a concept that is easier to understand and that does not require an ambiguity-resolving procedure. The FairVote organization supports the adoption of instant-runoff voting. The Ranked Choice Voting Act, supported by FairVote, would require instant-runoff voting in all federal House and Senate races. Like Condorcet voting methods, instant-runoff voting would also increase competition between parties and tend to favor moderates, although it does not always select the Condorcet winner if there is one.

It is important not to let the perfect be the enemy of the good. Any of these systems that allow voters to rank candidates in order of preference would generate a more moderate political culture. In addition to favoring the most moderate of a given set of candidates, the system would also influence what kinds of candidates enter politics in the first place. Given the distastefulness of our political discourse, many decent Americans have no interest in entering politics. That could change if the voting system removed a major cause of the culture war, the widening chasm between the two dominant parties. With a more civil politics, more decent Americans might consider running for office.

Often, people propose voting reforms because they will move the political equilibrium in their preferred direction. Proposals to elect the president by popular vote or to give statehood to the District of Columbia, for example, whatever their merits, are favored by the left and opposed by the right because they would shift political outcomes a bit leftward. It is worth emphasizing once again that any of these rank-ordered voting methods would be unlikely to shift long-run policy. They would simply cause more rapid convergence to the moderate policies we are likely to end up with anyway. Under our current system, the median voter wins on policy in the long run. This voting reform would merely end the ping-ponging between relative extremes that undergirds our culture war.

This culture war is dangerous. Even after the violence at the Capitol on January 6 ended, a majority of House Republicans voted to challenge the certification of electors. I found it sickening. While these members of Congress have no excuse for their actions, if circumstances were different we could see similar extremism on the left. If we do nothing, our culture war will continue and we will invite more instability. With a relatively small change to the way we vote, we would reduce extremism in both/all parties and stabilize our country. Have you had enough yet?

I vote for a different voting system