If the USA had direct plurality election of the president, what effect on the party system?

I know the 2020 election result–assuming the Senate majority remains Republican*–has ended any chance of serious electoral reform passing for the foreseeable future. But what if the National Popular Vote (NPV) compact were enacted? If there were no other reforms, the compact would result in the US President being elected by direct nationwide plurality.

Given the way assembly and presidential party systems work together in systems with powerful directly elected presidents, just changing to direct election in the USA could open up the wider party system in a way fully consistent with expectations from its existing electoral system. It is likely that direct election would lead to more presidential candidates winning votes, and that, in turn, would potentially lead to more parties in House elections, because the House party system is probably currently being restrained by how the presidency is elected more than by how the House itself is elected.

The House electoral system has seat product of 435. (The seat product of a single-tier electoral system is its mean district magnitude, times the assembly size.) Based on the Seat Product Model, the expected party system in the US House would have an effective number of seat-winning parties of around 2.75, on average, and a largest party averaging around 46.8% of the seats (about 204 seats). Of course, the actual party system has an effective number just below 2.0 and a largest party always above 50% of the seats. Do not blame the electoral system for the absence of other parties in American national politics. Even with single-seat plurality (in a few states, majority), the electoral system for the House should be expected to support more parties than what we actually have.

If we look at the worldwide dataset of presidential elections that Rein Taagepera and I analyze in Chapter 11 of Votes from Seats, the mean total for winning presidents under nationwide plurality is 48%. That is, of course, below the long-term average for US presidents, which is 52%, although it has trended downward since 1992 and averages around 49% over the past three decades, suggesting there is indeed some pent-up demand for more options. The leading presidential candidate typically wins more than the 48% that is the average in countries using direct plurality because the multi-seat plurality rule used at the state level in the electoral college normally suppresses third parties. And, unable to attract many votes in presidential contests, sustained party organizations beyond the top two are lacking. If they existed, they likely would compete for House seats as well.

It just so happens that a switch to direct plurality election of the president would be pretty consistent with what the existing House electoral system should be yielding! The estimates we have are: A president winning 48% on average (roughly what Hillary Clinton won in 2016, though with the electoral college that was not good enough); A largest party in the House having 47% of the seats. Based on other formulas in the Seat Product Model (SPM), the expected vote share of the largest party in the House then would be 42.5%, for an implied effective number of vote-earning parties of 3.13.

While it would be nice to have proportional representation of some sort for the House, it actually is the case that just changing to nationwide plurality for the presidency–as the NPV would produce–might be sufficient to “unleash” the House seat product and bring about a relatively more multiparty, but not significantly fragmented, House party system.

A quick comparative check of the data is in order, to see how these estimates compare to other countries’ experience. Across 117 presidential and semi-presidential systems (including, for the latter, only those with “strong” presidents), the mean share for the first-round or sole-round leading presidential candidate is 46.64% and the mean vote share for the largest assembly party in those same cases is 40.43%. Restricted to just pure presidential systems and those that elect their presidents by plurality (only 25 observations) we have 44.88% and 40.95%, respectively. So 42.5% for the largest vote share in US House elections is within the ballpark of other presidential systems’ observed experience; the set of cases from which I just reported average values has a mean seat product of 934.5, which is obviously higher than the US House’s seat product, and so they should be expected to have higher average fragmentation (smaller leading party) than the USA.

Additionally, Taagepera and I also have a model in Votes from Seats to estimate the effective number of presidential candidates (Np) from the assembly electoral system. It is Np=1.44[(MS)1/4 +1]1/3 (where M is the district magnitude–here 1, obviously–and S is the assembly size). For the US, this yields Np=2.55. We did not try to predict the vote share of the leading presidential candidate, but a rough approximation from that effective number would be 49.5%. Thus, roughly 48-50% for the president, on average, from direct plurality, plus a largest party in House elections in the ~43% vote range, seem like good educated guesses if the US were to change to direct plurality, by way of the NPV, even without any change in the House electoral system.

Given that reform to PR normally follows, rather than leads, an increase in vote share to parties other than the majors, it is even possible that the NPV’s anticipated effect on the wider party system could generate momentum towards House electoral reform. But that is beyond the scope of this planting, which was simply intended to show that the currently under-fragmented House (according to the SPM) could be brought in line with expectations simply by making presidential elections direct via plurality.

A couple of caveats: First, the exercise here reveals that the multi-seat plurality system of the current electoral college could be a major drag on the party system at the moment, preventing the House from having the party system its seat product could support. However, we should not ignore the Senate. Given that the Senate is a co-equal chamber, parties need to organize with this body in mind, as well as with an eye towards seat-winning potential in the House. And the Senate seat product is ridiculously small. Even if it were taken to be 100, based on the Senate’s total size, that would be small–roughly the size of New Zealand’s before its electoral reform in the 1990s. However, it is worse than that: I think its seat product actually should be coded as 33, as that is the normal number of seats at stake in any given election. And if we run the SPM on a seat product of 33, we get an expected largest party seat share of 65% (!). Obviously, the actual is already normally well below that, at least in recent times. So that suggests that the more “permissive” House electoral system is already helping keep the Senate less dominated by one party than the Senate electoral system in isolation would.

The second caveat is that primaries also reduce party-formation incentives to some unmeasurable but probably significant degree. But my working assumption is that ideological groups within the existing parties would bypass primaries for president if the latter were elected nationwide, and that the resulting new parties would want to show their flag in House elections, too, under such a scenario. Yes, of course, single-seat districts make life hard on smaller parties. But note that no single-seat plurality system in the world with a seat product greater than about 100 has a party system as dominated by two parties as the USA has. So small parties can find ways to win local pluralities. They just need to be unleashed. And plurality election of the president would help the House’s existing seat product do its thing.

Electoral reform is not happening soon. The NPV itself is likely off the table for now. Even if sufficient states (totaling at least 270 electoral votes) were to agree to enter into the compact, it presumably would take effect only with the approval of Congress. Thus as long as Republicans control the Senate, its chances are poor. Nonetheless, the issue will not go completely away (I hope!), and it is thus helpful to understand that just this one measure could break the dam of the rigid two-party system for elections to the national legislature, even without any reform of how the House is elected.


* Well, the Senate did not remain Republican, but even a year later, serious electoral reform looks dead nonetheless. It is just not a Democratic priority.

32 thoughts on “If the USA had direct plurality election of the president, what effect on the party system?

  1. Who knew? The USA also has parliamentary votes of investiture https://www.axios.com/gop-senate-biden-transition-50ebe6c8-e318-4fdb-b903-048908b3b954.html and, pending that, reserve powers https://www.washingtonpost.com/politics/trump-gsa-letter-biden-transition/2020/11/08/07093acc-21e9-11eb-8672-c281c7a2c96e_story.html, for the transition period between the general election and the new cabinet taking office.
    Like Batman and the Joker, we are not so different, you and us.


    • Both, perhaps.

      I mean, states could have their own party systems, as that is certainly the case in some other federations. And not all state legislators legislatures are small, though many are. It is an interesting question. I suppose if you have a complete two-party stranglehold on the national system it is rather hard to carve out a space at the state level.


      • Ha, I’m not sure the relative height of state legislators is of any relevance here!

        On a serious note, I see the Libertarians gained a seat in the Wyoming lower house – albeit in a district where no Republican stood.

        I think fairer, more uniform ballot access rules (for federal elections) and proper media coverage of third-party candidates are the key to unlocking greater partisan pluralism in the United States… but even then it could take a generation or two for the necessary cultural shift to occur.


      • In the bad old days of the 1980s, when the great state of Queensland was still known as the Deep North, the Honourable Russ Hinze was state minister of police, local government, main roads and racing. Hinze was not particularly tall, but was otherwise a person of immense size who became known as the Colossus of Roads. He avoided conviction for corrupt payments by the rather extreme legal strategy of dying, although his co-conspirator was convicted.

        In his advanced years Hinze divorced his first wife and married his young and beautiful electorate secretary. He arranged for a pink Mercedes to be delivered to his new wife as a gift on their first anniversary. Hinze spent the day calling her to see what she thought of the gift and wondering why there was no reaction. Sadly for the happy couple, his ex-wife had raced to the local motor vehicle registry and registered the pink Mercedes in her own name as soon as it was delivered to her.


      • Hinze was a larger-than-life populist figure who could quite easily have been a Boss Hogg-type character in Texas or, better, some Dixie State. He had absolutely no shame, eg once entered a “largest beer belly” (topless) contest at the Gold Coast while serving as a Minister of the Crown. Ironically his considerably svelter granddaughter Kristy Hinze was a well-known model a few years ago. There was almost zero resemblance between grandpere and grandfille but the surname was an immediate talking point in the media.


  2. Does this imply that, under the current system, third parties are more likely to be successful in smaller states than in larger ones?

    I think it does.

    And that’s true – Maine and Vermont have been the two states to elect third party candidates to statewide office in recent years (Sanders and King). Alaska has pseudo-third party candidates who get a lot of votes.

    California appears to have a lot of third party votes because of weird things that happen occasionally in their jungle primary system (if no Republican runs against a Democratic incumbent and no Democrat tries to primary them, then you get general elections that are Democrat vs Green or Democrat vs Independent, so the third party candidate can lose 80-20 and then say “20% for a third party isn’t bad”), but if you discount those, then all the interesting third party stories are in smaller states.


    • Interesting question. I had never thought that one through, but you raise a good point.

      Re California, that is not the system we have. No third-party candidates, or anyone else, make it to the November election unless they place in the top two in the first round (which is not actually a primary anymore).


      • To be, and surprising to me, 3 Libertarians, 1 Green, 1 American Independence, and a candidate indicating no preference managed to make it to the November ballot in the State Senate and State Assembly races. None seem likely to win.

        Considering how laughably small the California Legislature seems to be, I wonder if more could compete if they didn’t have nearly a half million people per seat in the lower house.


      • Sorry, that wasn’t especially clear.

        If you look at only “general election” results, for California (US House or State House/Senate), you occasionally see what looks like a very high number for a non-D/R candidate, but it usually arises when there is a Democratic incumbent in a very safe seat, and they were the only serious candidate to stand in the first round from either of the major parties – the Republicans presumably because there is no point contesting a seat where the Democratic party gets 80% or more of the vote, and the Democrats because a strong incumbent is nearly unbeatable, so potential contenders prefer to wait for an open seat race rather than get tainted as a loser. As a result, the second place in the first-round election goes to some independent or third party candidate (because there is no-one else standing, or because the other D/R candidates are not serious candidates), who then loses 80-20 or 85-15 or something in the “general election” against the strong incumbent.

        If you’re looking at just strong results for third parties across the US, you will occasionally see a result that looks like the third party is doing well, but, on further examination, it turns out that there was only one major party candidate, and losing by 30 points or more in a two-way race is not a good result. For instance, the Arkansas Senate race this year had a libertarian get 33% of the vote – because there was no Democratic candidate.

        My point was that the first-round system in California throws up these sorts of results a little more often than the conventional primary system.


      • Richard and Mark (and also Oliver, farther up-thread) raise interesting points about third-party candidates in contests that are not competitive among the two major parties. I have certainly noticed that in perusing results over the years–including very much in the earlier era of partisan primaries and multi-candidate generals. I’ve never seen anything that looked into the phenomenon systematically. It certainly is sensible that if one of the major parties does not run, or has a very “weak” candidate (unknown, even to partisans) a third party candidate can break through and end up in the 20-30% range or even win on occasion.

        I had missed that there were any contests in California in which a candidate from a minor party made it to the November runoff. Sure, we should expect that to happen now and then in uncompetitive districts, I suppose.


  3. Would you be willing to do everyone a favour and write a post on Benford’s law and the US election? The alt right has a bunch of videos and posts misusing it to suggest fraud in the US election. They are applying it to the first digit instead of the second or the last. What they’re really proving is polling station catchment areas aren’t random.


  4. The best immediate propects for increase in effective party size in the US is if Trump doesn’t take losing well at all, and implodes the GOP in the process, denying it what wd normally be easy wins in GA. If there’s more uncertainty about future elections and the HFC and the GOP break up into two different parties, effectively, then there’d be more scope for electoral reforms!

    Shugart, what wd be the implications if one used a 3 stage election for POTUS that would have MS of 49 in the 1st stage, MS of 3 in the 2nd stage and then MS of 1 in the last stage, after having used 435 3-seat PR elections to pick 1305 electors? I understand (49)^(1/6)=1.92, ‘n 49^(-1/8)=.61, but I’d predict that there’d tend to be 3 candidates from each of the 2 major parties and 1 other candidate so effective party wd be 2.6 and the size for the biggest party wd be .43. But then for the 3rd round, the effective party size wd be 1.2, which suggests that it’d be relatively strong chance for a major party to win all 3 seats in the 2nd round, which doesn’t matter when you’re doing a proxy-vote for the 3rd round…

    I know it’s just political science fiction, for now, but I think it’d be an interesting toy model for you to consider…


    • A supersized Electoral College with different thresholds required at each stage of voting sounds a lot like the German Bundesversammlung (Federal Assembly) to me.


  5. Re third parties in contests with one of the major parties missing: having mentioned the Libertarians, I should also include a Green near miss for the sake of balance. They appear to have come within 3.5% of beating the Democrats in an open seat in Maine’s 49th House district, with nobody from the Republicans apparently running (despite the GOP staging an uncontested primary earlier in the year).


  6. Query for Americans. I saw this quote recently, something I’d long wondered:
    ‘… The debate can essentially be boiled down to a disagreement over whether US elections are party-based or candidate-oriented. But that question has already been asked and answered, with the vast majority of political scientists treating as fact that Americans vote for the candidate, not the party. “In the United States, we have a candidate-centered system, people vote very much for the candidate from the local level, up to the statewide campaigns and federal elections,” said Paul Hernnson, a political science professor at the University of Connecticut, whose publications have focused on parties and elections. ..’ https://www.middleeasteye.net/news/us-election-democrats-centrists-progressives-blame-house-losses
    As an outsider, I can see why a “moderately long ballot” might encourage voters to vote across party lines. A Lincoln Project Republican in Utah can support Biden for President and Romney for Senate in a way that an anti-Brexit Conservative in England probably can’t. But most examples of US ballots I’ve seen (with the standard caveat that “it varies form state to State”) seem to be quite lengthy, with over a dozen separate offices. Moreover, there is usually the option to “vote a straight ticket” from president/ VP down to local councillors.
    Given this, it seems intuitively likely a priori that States with long ballots would see more party-centred voting.
    Is this the case in practice?
    (I don’t think any State has a particularly “short” ballot by world standards, but a State where Governor and Lieut Gov are chosen on the same ticket, where State executive officers, public university trustees, etc are not directly chosen, where each State Senate district votes only at every other election, and where there are fewer layers of local government and these use council-manager rather than strong-elected mayor systems, would be at the shorter-ballot end of the US… a fortiori if the State legislature were unicameral).


    • err, just re-read that… correct to “A Lincoln Project Republican in Utah can split their vote across parties (supporting Biden for President and Romney for Senate) in a way that an anti-Brexit Conservative in England probably can’t.


    • Tom, you quote someone musing about “the vast majority of political scientists treating as fact that Americans vote for the candidate, not the party.”

      I do not think that is so–either that the statement describes what political scientists say, or that it characterizes the reality. It is well known among political scientists that party is by far the strongest predictor of an individual’s vote. It has become more so in recent decades, with fewer and fewer voters splitting their tickets.

      Voters may still claim in opinion polls that they vote “the candidate, not the party”, but that is not how the vast majority are observed to behave.

      Yes, the rules make it possible for individual candidates to do better or worse than others of the same party in the same jurisdiction and election. There is still room for personal characteristics and record in office to matter. But the bigger story is the strong and growing party orientation of the electorate.


      • Oh, and Tom also asked about ballot formats. As for me, I have only ever voted in California, but in three different counties and numerous elections over decades. I have been presented with a wide variety of ballot layouts and voting mechanics. I have never been presented with an option to vote a straight party ticket.

        That is mainly because we use what is called the “office block” ballot. You must make a selection individually for each office in order to have a vote counted for it. There is never an option to just choose a party.

        In other states, where a “party column” ballot is used, there probably generally is a party-vote option. I would guess Ballotpedia or other online resources might have a list of such states, and potentially their different formats over time.


      • Straight ticket voting still happens in:

        South Carolina

        It was once much more common. The main push for its abolition appears to come atom the same party that pushes other vote suppression measures. Pennsylvania and Texas abolished in 2020.


      • The irony is that as ticket splitting has declined, states seem to be offering formal straight ticket voting less and less. Presumably some of this has to do with deliberate voter suppression, ws Alan says, but I wonder if there’s anything else behind it. The disappearance of hand counted paper ballots?


      • I’d think it is more likely the disappearance of the old lever-based voting machines. But I do not know if this potential explanation squares with the dates of abolition of the straight-ticket option, or the jurisdictions in which that has happened.


  7. Pingback: US House size increase: Inherently valuable? | Fruits and Votes

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