The Constitution gives states the power to conduct elections but does not specify their electoral system. It presumed that the English tradition of single-member districts where simple plurality wins would be standard nationwide. Given our present political impasse, we might reexamine this.

The old English first-past-the-post model has the advantage of rooting the elected representative in the district (or state) and giving citizens an individual to whom they can complain. It is simple and understandable. But it’s not very fair and can way overrepresent one party at the expense of another.

This is especially true when the district is gerrymandered. To a considerable degree, who draws electoral boundaries governs. Today, this means that in most states Republicans get more seats than their percentage of votes warrants. Gerrymandering could be cured by letting a computer draw district boundaries with the shortest lines — eliminating strangely shaped districts — but parties would fight it.

Our electoral rules strongly predict a two-party system. French political scientist Maurice Duverger elegantly demonstrated how single-member districts with plurality win almost automatically produce two-party systems. Suppose four parties compete in a single-member district. Party A gets 25%, B gets 25%, C gets 24% and D gets 26%. Winner: D.

Quickly, A and B recognize their advantage is to combine and win the next election. C and D must do the same. Result: two parties. The exceptions to this are countries where strong regional subcultures concentrate third-party voters: the Parti Québécois, Scot Nats and many Indian states.

Proportional representation (PR), used in most of Europe, has multimember districts that send people to parliament in proportion to their percentage vote. It places less premium on combining parties and so leads to multiparty parliaments, although recently this has settled into two big parties and a few small ones. Such systems usually require coalition governments, which are often prone to paralysis and breakup.

In PR, districts are based on population and voters choose among “party lists,” not among individual candidates. If party A wins 30% of the vote in a 10-member district, it sends the first three names on its party list to parliament. But what if party A gets 33% of the vote in an 11-member district, entitling them to 3.63 seats? You can’t send a fraction of a person to parliament so mathematical formulas apportion the fractional seats, giving a slight advantage to larger parties.

In addition, PR systems, to prevent parliament from splintering into too many parties, specify a certain threshold a party must reach nationwide to get any seats: 4% in Sweden, 5% in Germany. Israel had a mere 1% threshold, now raised to 3.25%, but still elects a dozen parties that make coalitions maddeningly difficult.

PR more fairly represents the electorate, but it breaks the close connection of individual legislators to their communities. How to have both? Germany’s postwar constitution fills roughly half the Bundestag’s seats from single-member districts and half from PR at the state level. Italy, Japan, New Zealand and Russia use variations of the hybrid German system.

France uses single-member districts but requires at least 50% to win. In most districts, this means a runoff election of the top two a week later. Maine and Alaska have added ranked-choice voting (used in Ireland and Australia) to their single-member systems. Also known as “instant runoff,” it could have recently saved Georgia much grief. Citizens get more choices and third parties get a chance, but it still tends mostly to two-party systems.

A compromise might be a “topping off” system that keeps single-member districts but corrects for numerical discrepancies. A state entitled to 12 congressional seats might have nine single-member districts. The remaining three would top off the state delegation to more accurately approximate the popular vote statewide.

Suppose Republicans in this state have gerrymandered the districts to give themselves five of the nine seats with only 40% of the state’s vote. The three at-large seats would then top off the Democrats’ four seats to give them a total of seven seats (out of 12) to closely approximate the 60% they won statewide.

Such a system would be fairer and undermine gerrymandering; there would be less incentive for it. Statewide representatives could also bring to Congress a broader vision of politics than their home counties. That state’s ruling party, however, would fight anything that cut their grip on power. Don’t count on them doing what’s right or fair, but a referendum might.

If you really want to give third parties a chance, you could give a seat or two of the topping-off seats to small parties that have reached a threshold of, say, 10%. People inclined to Libertarians or Greens would thus not be throwing away their votes; they deserve representation. The American electorate is too complex for just two parties, both of them ungainly coalitions of barely compatible factions.