The strategic voters’ nightmare that is US Democrats’ “proportional” system

With a “front runner” who so far is not mustering more than a quarter of the vote in polling aggregates (e.g., both Fivethirtyeight and Economist), and four other candidates in the 10%–20% range (here with some variation between different aggregators), it is a good thing the Democratic Party uses proportional representation to choose its nominating-convention delegates. Right?

Well, not this “proportional” system. I will now leave aside those zany rules of the Iowa caucus or the marginally more rational rules of the Nevada caucus, and focus on the closest thing we will get to a national primary: “Super Tuesday”. Specifically, I will focus on California for the the obvious reason that it is the biggest. And happens to be where I live and vote. Other states have broadly similar systems, but for smaller numbers of delegates.

This is one awful example of “proportional representation” (PR). Why? First, because it is not really PR due to the high threshold. Second, because it is ridiculously complex. Third (and flowing from the first two), because it is nearly impossible to know how one should make effective use of one’s vote.

My premise is to assume a voter wants to vote against Sanders. (Any resemblance to any particular actual voter may be coincidental. Or not.) With so many candidates still in the mix, one could at least feel good that it in a big state with a lot of delegates, the proportional allocation will mean your vote is not wasted. It could help select some delegates for whichever non-Sanders candidate the voter selects.

But that is not the case at all.

First, there is the threshold. It is set at 15%, which is extremely high. It is all the worse when, as noted already, so many trailing candidates are at risk of falling below 15%. It is not out of the question that all of California’s delegates could go to Sanders even if he has just 32% of the vote, as in a recent PPIC poll. That poll has Biden in second with only 14%. A delegate sweep is not the most likely outcome (8% are undecided, and many might be weakly supportive of their current choice and thinking strategically, like our hypothetical voter), but it is possible. One hundred percent of the delegates on a third of the vote certainly would not be a  “proportional” outcome!

Then there is the districting. Obviously, we know from studies of electoral systems for actual proportional representation systems that having many districts, and low-moderate district magnitude (number of seats–here, delegates–per district) reduces proportionality. On the other hand, if a candidate is just below 15% statewide, the districting might help that candidate, to the extent that there is regional variation in support. Failing to clear the statewide threshold does not preclude getting delegates in a district, as long as the candidate is above 15% in any given district, and that the magnitude of that district is large enough for the candidate to get a delegate with whatever his or her vote share is in the district.

The statewide delegates amount to around 35% of all the delegates awarded in California: 144 of the 415 total. In electoral system terms, the allocation is in parallel, not compensatory like many two-tier proportional systems. That is, a candidate who clears 15% gets a “proportional” share of the statewide delegates and adds on to this whatever number of delegates he or she has won in districts.

A statewide district of M=144 seems huge, right? Well, this being the Democratic Party, they have to make it further complicated. There are two statewide districts, in parallel with each other as well as with the many sub-state districts. The magnitudes are still large, at 54 and 90. (The former are the PLEO, or pledged leaders and elected officials.)

The districts for delegate selection are the state’s districts for the US House. They vary in magnitude for delegate purposes according to recent Democratic voting history in the district. California has 53 districts, and they vary in magnitude from 4 to 7. There are only two districts (numbers 12 and 13) that elect 7. The mean magnitude is 5.1. See the California Democratic Party Delegate Selection Plan (pp. 14-15 of the linked PDF) for the number per district.

(The Plan has no description of the specific allocation formula that I could find, but maybe I missed it; see also GreenPapers.)

So what should our totally hypothetical anti-Sanders voter do? Ideally, figure out which of the other (acceptable) candidates is above 15% in his or her district. Better yet, figure out which one might be marginal for a delegate. That would be a strategic vote based on local support and the district’s magnitude. But it is not as if such information is widely available. One can guess off district demographics, or noisy signals like local offices for the campaigns or yard signs, etc.

The PPIC poll has a regional breakdown within California. But the “regions” are blunt categories–Los Angeles, Other Southern California, SF Bay Area, and Other. There is some considerable variation, even with the caveat that we have 53 districts but four regions. Sanders leads in Los Angeles with 36% and the next up is Biden, at 16%. In Other Southern California they are on 41% and 15%, with Buttigieg also on 15% (the latter supposedly has just 9% in LA). SF Bay Area also has Sanders leading with only 31% and the next closest is Warren at 18% and then Bloomberg at 14%. If, like me, you are in “Other” it is really a mess! We have Warren 18%, Biden 17%, Sanders 16%, Buttigieg 14% (also 11% unknown, higher than other regions). Of course, a lot of these are in the margin of error of the threshold, and each other, and further district-level variation within each region is likely.

So maybe the best is just to figure out which ones are likely to be close to, or “securely” above 15% statewide. Forget the district, and focus on those two large magnitudes at the state level, in which small vote shifts for above-threshold candidates actually could change the delegate totals.

The previous numbers are based on only one poll, of course. There is too little polling of this state. The FiveThirtyEight estimate for California is a little different: 27% Sanders, 16% Bloomberg, 14% Biden, 11% Warren, 10% Buttigieg. (The total for all listed candidates gets us to 89%, so 11% undecided.) Given the paucity of polling, these estimates are based not only on polls, but also on national trends adjusted for state demographics. And, as noted earlier, it risks no one but Sanders being over the threshold, even if that is not in the end a likely scenario, in part because allocating or removing undecideds likely puts at least a couple of other candidates over 15%. Plus, as mentioned, there will be some degree of regional variation that can make a sub-15% candidate statewide be well above that level in a district. But also, remember: many districts have a magnitude so low that even 15% locally would not be enough for a district delegate!

Or there’s voting sincerely. What a concept. Since I don’t like any of these candidates, that would mean staying home. But I don’t want to do that!

31 thoughts on “The strategic voters’ nightmare that is US Democrats’ “proportional” system

  1. Seems like they’re intentionally trying to make it harder for people to vote against the front-runner so that the primaries don’t stay competitive for too long…


    • Never put down to conspiracy what can be explained by sheer bloody-minded stupidity. There are far easier ways to design an electoral system to favour the frontrunner, notably the Republican Party, which uses a must less ‘proportional’ system. When the McGovern commission advocated proportional delegate selection, they might have consulted the already extensive literature on proportional representation and noted that systems with high arbitrary thresholds produce highly disproportional results, but they didn’t and decided to reinvent the wheel instead.


  2. Fifty years ago, when I was a young member of the Democratic Labor Party, I knew of three voting system – first past the movable post, preferential voting (also called alternative vote and instant run-off) and proportional representation, which as far as I knew meant the Australian Senate system; i.e., the single transferable vote. Naturally enough, as both a democrat and a DLP member, I thought PR (STV) was the best system possible. Not too much later, I learnt that there were list systems of PR too. It was many year before I came across this site and discovered all the weird and wonderful voting systems mankind has come up with. A true cornucopia of complexity and disproportionality lies in wait for anyone who ventures into the jungle of voting systems. The US Democrats – the capital “D” distinguishes them from democrats – seem to have taken the gold medal for complex disproportionality.

    If there were not to be national direct primary, it would be simple to create constituencies of 300,000 Democrat voters, each electing nine delegate to the national convention. District magnitudes would be the same, except a rule could prevent the convention districts crossing state borders, in which case they would be as nearly as mathematically possible the same. Congressional boundaries are so gerrymandered that ignoring them would not trouble community sensitivities. Delegates would be elected by the single transferable vote and would have to be vote for the presidential nominee they were pledged to until he or she dropped out voluntarily or was eliminated at the convention. The quota for election would be 30,001 votes. Voters would indicate preferences so voters for candidates with very little support would transfer to those with more support, thus not wasting their votes or having to vote strategically. If a quota of 10.0003 per cent is thought too high, it could be replaced with one of 7.1428571428571 per cent in 14-delegate districts.

    The convention delegates would choose the presidential candidate by exhaustive ballot, with the candidate with the least votes dropping out at each stage and his or her delegates being free to vote for anyone else at that stage. I don’t have a problem with super-delegates, provided they make up a small percentage of the total and don’t get to vote unless the convention has not given a clear endorsement at an early stage of balloting.

    The problem with my system is that it is simple, fair and democratic, so it is has no chance of adoption.


    • I see absolutely no need for districts below the level of the states at all. They would add an unnecessary complication and another locus for the unique US talent for electoral snollygostery. I know you re concerned with different quota in districts of different sizes. Even in the Australian house of representatives, where districts have the same magnitude and are generally very close to equal enrolment, there are quite marked variations in the quotas because of variations in turnout and informal boating. For example in May 2019 the quotas for seats in the ACT and the Northern Territory were markedly different because of enrolment variations and the much higher informal vote in the NT.


      • Alan,

        I think a variation in percentage quotas matters a lot, and, the bigger the variation, the worse it is, but, your proposal is still infinitely better than what the Democrats have now.

        PS I think “informal boating” is the best form of boating too.


  3. Assuming that the Democrats want to retain the 15% threshold to encourage candidates with little or no real prospect of winning the nomination to drop out (remember that this is ultimately a single-winner election, not a 3979-winner election for convention delegates), then the simplest thing to do would be to allow preferential votes (“ranked-choice”) and eliminate the lowest-polling candidate and do transfers until every remaining candidate has at least 15%.

    Also, scrap the idiocies of the district and PLEO sections and just allocate each state as a single large proportional block.

    If our hypothetical voter could vote for, say, Warren 1, Buttigieg 2, Biden 3 (or whatever their preferences are amongst those candidates) then they would be reasonably confident that their vote would be allocated to a candidate who would get over the threshold to 15% or more.

    Especially if the quota is recalculated at each stage on the active vote (ie treat votes whose preferences are exhausted as being abstentions for the purposes of recalculating the quota).


    • Your plan would make sense if and only if there were ever only 2 candidates for the nomination. You are making the same error as the authors of the XII Amendment, who assumed the majority would always prevail because there would always be only 2 candidates for the presidency.

      You could, I suppose, organise the Democrats into formal factions so that you only ever had a binary choice between a single Left Democrat candidate and a single Centre Democrat candidate. If that system applied the Centre Democrat candidate would be romping home in the present contest. However, a faction system would only raise the question of how to run nomination contests within the two factions.

      No system of preferential voting uses an arbitrary threshold. It is not logically tenable to call for preferential voting and then describe a system that is clearly not preferential voting and which, moreover, is not a single winner contest as you claim because your proposal produces more than 1 winner. The test for viability should be the election of delegates and the Droop quota would guarantee that without an arbitrary threshold.


      • It seems like you’re supposing the eliminate continues until some natural quota is reached, but I don’t think that’s the proposal. It stops the moment every candidate remaining is above the artificial threshold, and then allocates according to some list like process.

        An example. 218 delegates to distribute, several lead candidates. Vegemite is love-it-or-hate-it, but a majority would be willing to have fruit or icecream for dessert. No-one quite knows who will get above or below the threshold. Maybe Misc1-3 are groups of irrelevant candidates.

        12% Banana > Apple > Icecream > Vegemite > Misc 1 > Misc 2 > Misc 3
        11% Apple > Banana > Icecream > Vegemite > Misc 1 > Misc 2 > Misc 3
        10% Icecream > Banana > Apple > Vegemite > Misc 1 > Misc 2 > Misc 3
        10% Icecream > Apple > Banana > Vegemite > Misc 1 > Misc 2 > Misc 3
        10% Vegemite > Icecream > Apple > Banana > Misc 1 > Misc 2 > Misc 3
        10% Vegemite > Apple > Icecream > Banana > Misc 1 > Misc 2 > Misc 3
        10% Vegemite > Apple > Banana > Icecream > Misc 1 > Misc 2 > Misc 3
        10% Vegemite > Banana > Apple > Icecream > Misc 1 > Misc 2 > Misc 3
        6% Misc 1 > A > B > I > V
        6% Misc 2 > I > B > A > V
        5% Misc 3 > V > B > I > A

        Round 1:
        40% Vegemite
        20% Icecream
        12% Banana
        11% Apple
        6% Misc 1
        6% Misc 2
        5% Misc 3

        Eliminate Misc 3. Round 2:
        45% Vegemite
        20% Icecream
        12% Banana
        11% Apple
        6% Misc 1
        6% Misc 2

        Eliminate Misc 1, 2. Round 3:
        45% Vegemite
        26% Icecream
        17% Apple
        12% Banana

        Eliminate Banana. Round 4:
        45% Vegemite
        29% Apple
        26% Icecream

        All remaining candidates have 15% or more. Delegates allocated:

        Vegemite — 98
        Apple — 63
        Icecream — 57

        Those who want fruit for dessert send 63 delegates to the convention. This is a lot better than what they would have got under some non-preferential system, when they would have sent a mere 0 delegates. Those who want something sweet for dessert send 120 delegates, compared with 72.

        It seems like a coherent and logically valid procedure. It probably tends towards filtering out candidates if there’s no Super Tuesdays too soon. (Iow, if someone’s in a fruit favoring state that comes after this state, they are now more likely to switch from Banana to Apple, since they would rather a fruit get a majority to avoid the risk of defection to Vegemite.)


      • “No system of preferential voting uses an arbitrary threshold…”
        Up to a point, Lord Copper… Assuming that by “arbitrary” you mean “other than the applicable Droop Quota”, here are three counter-examples from memory:
        (a) Canadian House of Commons uses runoff ballots to elect its Speaker but also summarily excludes any candidate with under 5% support.
        (b) South Australia’s former upper house closed-list-PR system (1973-1985) summarily eliminated all lists under half a quota of first preferences (with 11 seats and Q = 8.33%, this meant 4.1667%) and then redistributed their votes among the lists over the threshold. Droop quota with largest remainders. As I’ve noted before, this created a risk that if you voted for a list polling 0.501 > < 0.999 quota, your vote could be binned if your favoured list had too few votes to be excluded and its votes transferred, but too few votes for a full quota or one of the lucky largest remainders.
        (c) Cambridge, Massachusetts summarily excludes any candidate with fewer than 500 first-preference votes. I have heard this was because when that city adopted PR-STV, it also abolished the requirement of 500 signatures per nominating petition. Preferential voting was meant to remove the danger of candidates with only a dozen or so nominators splitting the vote. So, this threshold was a quid pro quo trade-off. I suppose on the same logic you could say Australia’s Senate PR-STV system has a 50-voter threshold, although conceivably 50 friends and neighbours might sign your nomination if you pester them but then not vote for you when they get a secret ballot. Am fairly certain there have been Australian Senate candidates who polled fewer first preferences than the number of signatures required to nominate (Chris C? Henry?).

        PS: I also have some dim recollection that for a short time after 1989, Czechoslovakia and/or the Czech Republic allowed preferential voting among party lists, with a 5% threshold.


      • lazaro

        You have developed something very close to the Modified D’Hondt system used on two occasions in the ACT. I am not sure the US, or anywhere else, is ready for primary election results that take 6 weeks to count.


      • Tom

        None of those thresholds approach the size of the McGovern threshold. I went to some effort to establish why the Droop quota is not an arbitrary threshold. You may care to address why the quotas you mention are.


  4. Yes a nightmare. In addition there is ambiguity in the party rules ( “Delegate Selection Rules” link) for district delegates. Only in the two districts that have 7 delegates (#12 and #13) would a candidate who gets 15% of the vote be sure to get any delegates, since .15 X 7 is 1.05 but in all other districts is less than one. It is unclear how ties are to be handled — for instance if 4 candidates get 15% each and one gets 40% in a district that has 5 delegates — one of the 15% candidates would need to go empty handed.

    The underlying problem is the failure to use a ranked choice system (both for the Democrats this time and the Republicans in 2016).


  5. Given your sincere desire is for Anyone But Sanders, but you are prohibited from voting for Anyone But Sanders, my recommendation is to look at the national polls the day before you head out and vote for whoever comes closest to the top, other than Sanders. Maybe they’ll get quotaed out of your district, but it might help them bandwagon their way to success anyway.

    Or else find out who your friends are voting for and copy them.


  6. I have had an idea of a different kind of threshold: a seat (or delegate) threshold, instead of the more traditional vote threshold. After an election, all parties can participate in an initial provisional/hypothetical seat allocation, be it by Saint-Lague, D’Hont or whatever. Then all parties with zero seats are dropped. If all remaining parties have X number of seats or more, where X is the threshold, the provisional allocation is then the actual allocation and the parties go home with all these seats. If there exists parties with fewer than X seats, then the party with the fewest votes is dropped, and a second round provisional allocation is performed on all the remaining parties, and check again if all remaining parties have at least X seats. Repeat until all remaining parties have at least X seats.

    I suppose the procedure can work with a vote threshold as well, i.e. successively dropping the smallest party until the smallest remaining party have Y% of total votes obtained by all remaining parties, where Y% is the threshold. But I like the seat threshold since it adheres more closely logically to the original intent of thresholds, i.e. to prevent excessive fragmentation of the legislature. Anyway, barring an arbitrary threshold coupled with preferential voting – which I myself am not personally averse to – this could be an idea to prevent excessive wasted votes arising from the traditional vote threshold.


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  8. Pingback: The Magnitude of Sanders’ Win – Oligarchs In Charge

  9. So, the candidate who got a mere quarter of the votes in Iowa, a mere quarter of the votes in New Hampshire and mere third of the votes in Nevada is the frontrunner. We are told that he may build up such an unassailable lead in delegates, even though that lead still leaves him with only 40 per cent of them, that he may be unstoppable as the chosen one. If that does not get the Democrats’ establishment to learn what proportional voting is, nothing will.


  10. Lots of good ideas for change here. I’d like to put in one suggestion that seems the most obvious to many of us outside the US: a national party should have one set of rules for selecting delegates to a national convention, not different rules for each state. I know this flies in the face of US historical practice, and it’s never going to happen. But it seems to me it’s the one thing that will always put the brakes on meaningful reform.


    • I think it would be advantageous for a party to have a 3-stage 6 week process for its selection of a ticket, using 2 national votes and 1 proxy-vote. The first stage(2 weeks) would use 7-seat PR to pick 7 diverse candidates. The 2nd stage(3 weeks) wd have everyone pick which 3 they want to go to the final stage, and also help pick use 3-seat PR to pick their delegates for the final stage. Then, the 3 finalists would all choose a veep from one of the other 6 candidates in the 2nd stage and then meet with the delegates who would within a week determine the next ticket.

      That wd be consistent across states and it would reward empathy and tend to reconstruct a center for the party. One could even let anyone but members of the other major party participate in the first 2 stages, but not as delegates.


    • I warble on a bit about reinventing the wheel, but there is one great disadvantage to the practice. When we talk about MMP or STV we all have a fairly precise idea of what either system looks like. No-one has a precise idea of what high threshold variable magnitude high disproportionality proportional representation looks like so its a whole new enterprise to critique the 50 different versions of HTVMHD.


    • Actually, the Democrats impose considerable uniformity on the rules for states, although obviously the option for caucus or primary is significant discretion. Republicans have more state-by-state variation in rules.

      (This was a response to Doug’s comment from 25/02/2020 at 8:19 a.m.)


      • I actually read, with mounting disquiet, the Democratic delegate selection plans for Iowa, New Hampshire and California before I commented above. All three instruments provide they must be read with the national rules. There is enough variation in them, even allowing for the caucus in Iowa and the primaries in the other states, that any campaign would need legal counsel to study all 57 plans to maximise their chance of getting delegates. A single national rule would be far more transparent and small-D democratic.

        In all three the language is ambiguous, arcane, verbose and sesquipedalian. Just quietly, if I were a first year law student doing a plain English drafting course I would not dare put any of them up as an assignment.


  11. Pingback: Super Tuesday district magnitudes | Fruits and Votes

    • One could keep the 15% (or other high) threshold to winnow the field while at the same time instituting rank choice voting. RCV would deal with a secondary point in the Time article: “But on the face of it, rule 14.B seems to disenfranchise many voters. Of the 13.7 million votes cast in the Democratic primaries thus far, not including the Iowa and Nevada caucuses, TIME estimates that more than 354,000 went to candidates who did not meet the 15% threshold.”


      • Or one could not. While RCV would be an effective way to choose delegates, RCV, as discussed in previous threads already has a threshold in the Droop quota.

        The 15% threshold is an arbitrary figure that is very high by the standard of any system of proportional representation. Its effect is not to winnow the field but to induce an extraordinarily high degree of disproportionality into delegate selection, such that one could almost argue that that the main characteristic of this chimera, which MSS described in a previous thread as ‘zany’ is high disproportionality.

        The Time example of an alternative 1% threshold is frankly just choosing a ridiculously extreme example as a way of propagandising the 15% threshold.


    • Wikipedia has a list of electoral thresholds. Only Turkey, Liechtenstein, Andorra and Kazakhstan have thresholds higher than 5%. Leaving aside the two microstates, where electoral systems tend to be somewhat sui generis, the Democratic party’s sole exemplars for such high thresholds are the democratic paradises of Turkey and Kazakhstan. Only Turkey has a threshold higher than 7%. Perhaps the 15% threshold could be renamed the Erdogan number.


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