Proportional Electoral College, Why Not?

A lot has already been said about the 2016 US Presidential Election. It was hateful. It was sexist. It was divisive. It was social media vs news media vs fake news media. It was populism vs “establishment-ism”. And many more things. As different as this election was from previous elections, it was also similar to many elections — the strategic campaigning to net the most Electoral College votes.

For simplicity and brevity, the President of the United States is not decided directly by popular votes — that is whoever gets the most votes, is elected president. Instead, there is the Electoral College, comprising of 538 total electoral votes divided among the 50 US states and the District of Columbia. Each state is allotted a certain number of electoral votes. For each state, the candidate who receives the most votes, is then awarded that state’s electoral votes. [There are some technicalities, but this is out of scope for this article.]

From Wikipedia here is how the Electoral College votes were distributed.

One of the complaints is that Hillary Clinton received the most popular votes of all candidates, yet still lost the election. In this way, the “will of the people” was not reflected and as a result there are calls for abolishing the Electoral College. On the other hand, defenders of the system say that the Electoral College was not a sudden revelation, and that Hillary Clinton’s campaign failed to focus on the “correct” states. And so it goes.

Other criticisms are that as an unintended(?) consequence of the electoral system, campaigning tends to get focused on “swing” states — states that are not high probability Democrat or Republican leaning. What this leads to is a “reduced dimensionality” in the voting system in that not every vote counts and not every state counts. For example, votes for a Republican candidate in California, which for a long while has voted Democrat, actually don’t matter and never will matter short of a major social upheaval; Republican votes in California have a weight of zero. Texas works similarly but at the expense of Democrat candidate votes.

We can argue that since the President is elected via a winner-take-all system, eventually one set of votes won’t matter. But does it need to be multiple stages of winner-take-all?

One thing that has puzzled me is why, on a state-by-state basis, the electoral votes have to be winner-take-all. What if electoral votes were distributed based on the proportion of votes each candidate received in a given state?

Here’s a proposed revision using Michigan, a key swing state where Donald Trump won by roughly 11,000 votes, as an example. Below is the vote distribution for Michigan as of 12/3/2016 as given on Wikipedia.

Party Votes Percentage
Republican 2,279,543 47.50%
Democrat 2,268,839 47.27%
Other Independent 250,902 5.23%

Michigan commands 16 electoral votes, all of which went to the Republican candidate. I propose that instead of winner-take-all at the state level, electoral votes should be proportionately distributed. Since, we would probably want to keep the votes as integral values, I would suggest that candidates receive the greatest integer less than or equal to the product of the total electoral votes that are possible and the proportion of popular votes they received with the “unaccounted” votes going to the candidate who won the state’s popular vote. In equation speak this means that Donald Trump receives
$$\frac{2279543}{4799284}\cdot 16 = 7.5996102752 \mbox{ electoral votes before rounding down}$$
Hillary Clinton receives
$$\frac{2268839}{4799284}\cdot 16 = 7.5639249521 \mbox{ electoral votes before rounding down}$$
and the independent parties [for sake of this example, I am lumping all third-party candidates into one category: “independent”] receive the remaining 0.8364647727 electoral votes before rounding down.

That was the proportional distribution. Next, we round down [greatest integer less than or equal to …]. This means that Donald Trump receives 7 electoral votes, Hillary Clinton receives 7 electoral votes, and the third-parties in the aggregate receive 0 electoral votes. This tallies to a total of 14 electoral votes, leaving 2 votes unaccounted for. Since Donald Trump received the most popular votes, he receives the remaining 2 electoral votes. The final breakdown then gives Donald Trump 9 electoral votes and Hillary Clinton 7 electoral votes.

If we apply this reasoning on a state-by-state basis for the whole country, we see a different split of the Electoral College. In this version, Hillary Clinton gets 268 votes, Donald Trump gets 266, and the third parties get a combined 4 votes, with Gary Johnson getting 2 electoral votes (TX and CA), Jill Stein getting 1 (CA), and Evan McMullin getting 1 (UT).

Here is how the votes would break up by state in the format of “Democrat (Blue) / Republican (Red) / Other (Green)” for the three numbers that appear on each state.

What’s interesting here is that no candidate gets the majority 270 electoral votes, which means that a secondary process is needed to declare a winner. Fortunately, we have rules in place for such a situation.

But what’s even more interesting and important is that now, there is a real incentive for every individual to vote in their state — namely, every vote for a candidate helps to secure a little bit more of the electoral votes available. Currently, and as an example, if I am a Democrat voting in Alabama, my vote is effectively useless, since 62% voted Republican. However, with a proportional distribution of the electoral votes, as a Democrat in Alabama, I know that my vote will do something positive for the candidate that I want to support. Similarly, if I vote Republican in California, my vote as it stands does absolutely nothing. And as mentioned above, short of a major social upheaval, my vote will never do anything in California. However, with a proportional distribution of electoral votes, all 55 votes won’t automatically go to Democrats. Heck, we can see that 2 actually went to third party candidates.

Campaigning now becomes a completely different game. Candidates can’t simply ignore their “safe” states, nor will the election have to focus exclusively on a few swing states. States like Florida won’t be 58 point moves. Now they’ll be at best 4 to 6 vote swings. There is a little more stability.

Of course, polling becomes much more difficult and much more important. Each state matters. As I said earlier, the current system is low-dimensional. We don’t really have 50 states (and DC) in the election process.

To be clear, the modified map I gave above is an exercise to see how the votes would have panned out if we applied a proportional allocation of the electoral votes, a posteriori. I think that the voter engagement would be much higher in each state solely because each vote does something positive for the voter’s candidate. Vermont, for example, is 3/0/0 in favor of Democrats with a 56% / 30% / 14% split among Democrats / Republicans / Other voters. How many Democrat voters simply didn’t bother to vote because they knew that their state would go their way? The same question can be asked of Republicans in Republican strongholds. And how many voters didn’t bother because they knew that their state wouldn’t go their way?

Finally, some math speculation. Emphasis on speculation.

Why Wasn’t It This Way To Begin With?

I’ve wondered why a proportional distribution of electoral votes wasn’t the system to start with. To me (naturally), it makes the most amount of sense and is far more fair than the current set up of state-by-state winner-take-all. Then it dawned on me. This was a system set in place well before our high precision calculators. Heck for the better part of the 20th century, banks and financial institutions calculated compounded interest on a 360-day year, because the math was “nicer” than 365. The former has a lot of good divisors [2,3,4,5,6,8,9,10,12, etc.], whereas with 365 we’re kind of stuck in the mud with [5 and 73].

So, similarly, I can imagine that in the 19th century, doing this calculation by hand was very tedious.
$$\frac{2279543}{4799284}\cdot 16 = 7.5996102752$$
Of course, it can be done and there would have been mathematicians then who would have done this. But why bother with this brain damage when a far simpler solution that is transparent to the overwhelming majority of voters is to simply have winner-take-all on a state-by-state basis? The math is much simpler — which pile is larger? Whoever has the larger pile wins.

Anyway, there is a larger question to ask — should we or shouldn’t we simply move to a popular vote, winner-take-all election? There is great debate on this matter, but in the meanwhile, I feel that the proportional distribution of electoral votes is a strong compromise between proponents and opponents of the Electoral College. It will, by and large, reflect the popular vote with a much smaller risk of “inverted” elections like that in 2000 or in 2016. Every vote in every state will matter equally [but nationally, some votes will still mean more than others because the population count to electoral vote ratio is not uniform across all states].

Your thoughts? Should we distribute the electoral votes proportionally?

[edit: The always-helpful Colin Beveridge (@icecolbeveridge) points me to D’Hondt’s Method, which is a method for proportionally dividing votes. Here’s Colin’s article.]

[edit 3/21/2019: As I’m seeing this post start to trend in the wake of comments by Elizabeth Warren, keep this in mind: this was written in 2016 as mostly a musing and thought exercise about “what if we did it this way” … I’m not writing a book here. It’s a blog post and there is obviously a tremendous amount of nuance here. No system is perfect and even the straight national popular vote will have its unintended consequences. We’re a high-dimensional society and the more we keep thinking that the vote system winner should make decisions, the more fractured we will become. While statistically, a 51-49 win is a crushing victory when we have 100 million+ votes, 49% of the population is not to be “ignored” or somehow marginalized. So long as the winner (by majority or by electoral college chicanery) thinks they have a mandate, the more fucked we will be. Take your anger elsewhere and work on the reform you are seeking.]

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17 thoughts on “Proportional Electoral College, Why Not?

  1. Ron Schnatzmeyer

    I’ve been in favor of a proportional system since the Florida 2000 fiasco. All of that mess wouldn’t have happened if a proportional system had been in effect.

    With all due respect, It appears to me that the math is over complicated with all of those decimals. I suggest a more integer approach. Using your example from Michigan:

    The other candidates did not receive enough for even 1 electoral vote, therefore their 250,902 votes should not figure into the calculation and are discarded.

    Republican 2,279,543
    Democrat 2,268,839
    Total 4,548,382 eligible votes

    4,548,382 / 16 electoral votes = 284274 (rounded to the nearest whole vote) = 1 EC vote

    Republican 2,279,543 / 284274 = 8 remainder 5351
    Democrat 2,268,839 / 284274 = 7 remainder 278921
    The candidate with the greatest remainder gets the last one.
    Result: Trump 8, Clinton 8.

    When calculated out to all states the results are close to yours. I came out with 265 Trump, 268 Clinton, 3 Gary Johnson, 1 Evan McMullin, 1 Jill Stein. If I exclude the third party candidates I get Trump 268, Clinton 270.

    One obvious problem is that just a few third party EC votes can prevent anyone from getting the required 270. A proportional system would make this more likely. With the close elections these days we certainly don’t want to implement a system that would throw every election into the House of Representatives. So since we’re just pondering here, maybe only the two receiving the greatest votes qualify for the electoral college and the rest are discarded. That would make sense as the constitution gears the election to ((total-electors / 2) + 1) .

    Another push-back I get frequently when discussing a proportional system is that no matter how you apportion the electoral votes the electoral college is inherently unfair because an EC vote does not represent the same number of people from state to state. That is objectively true, but a proportional system does tend to level that out. That goes nowhere however with those who insist on a straight popular vote. I’m not really sure how to answer that one.

    I am convinced though that a proportional system would bring in more participation nationally and give those in the smaller states at least an equal influence. We’d see candidates all over instead of just the states with the most people.

    Anyway, Since you asked for my thoughts, here they are.
    Thanks for letting me share.

    1. Manan Shah Post author

      Yeah, I think there are many ways that this can be worked out. One thing I’m not sure of is why the unassigned ECs would go to the candidate with the greatest remainder. I’m of the opinion that the unassigned ECs should go to the candidate with the most votes. That would be consistent with the idea of voting.

      I do agree that the tiebreak rules need to be revisited. I would be ok reassigning the EC votes of 3rd place and below candidates to the top two candidates. And in the event that or otherwise ends up with a 269-269 split, then I’d be willing to go with total votes as a tiebreak at which point the probability of a tie is extraordinarily small.

      1. Ron Schnatzmeyer

        Why does the last unassigned EC vote go to the one with the largest remainder? In the example, the first 15 EC votes were assigned exactly equally at 284,274 popular votes for each 1 EC vote. The last EC vote essentially comes down to a contest between only the remaining unassigned popular votes which in this case is A) 5,351 votes to B) 278,921 votes. You can’t reuse the already assigned votes. Therefore, the one with the highest remainder has the greatest number of votes for the last remaining 1 EC vote. B gets it. That’s my logic for it anyway.

  2. Robert

    I was wondering if a “first pick-second pick” ballot combined into the proportional ballot might make sense. First pick could help with third party recognition and second pick could help tie-breaker situations. That way third party voters could vote their conscience and possibly advance that party while the tie-breaker/runoff vote would allow the same voters to avoid “sapping” the “lesser of two evils,” and possibly even prevent inverted elections… All on one ballot.

    1. Manan Shah Post author

      Yeah! One of the ideas I’ve had dance in my head was allowing a voter to split their vote. Say there are three candidate, R, D, I. Maybe I can do something like 40% of my vote for Republican, 40% of my vote for Democrat, and 20% of my vote for Independent. Rather than forcing an individual to choose one side, they can express their opinion of how much they agree with each party my distributing their vote proportions.

  3. AMH

    I really do like the theory of this idea; especially because it makes minority votes in each states count, but also because it allows for third party penetration. An emerging third party can garner concrete electoral results that may increase over time to produce a consequential party.

    HOWEVER, any penetration by third party candidates greatly decreases the likelihood of one candidate receiving a 270 majority — like you show here for 2016 election, and I believe may also have been the case in 2000. So that throws us into the obscure electoral college rules to determine the final outcome (which I never knew about before linking off your post). Have you looked at that and followed the result all the way through? It says:

    “If no candidate receives a majority of Electoral votes, the House of Representatives elects the President from the 3 Presidential candidates who received the most Electoral votes. Each state delegation has one vote.”

    Each state delegation has *one* vote, which presumably would go to the popular vote winner of each state. That is an even worse version of winner-take-all; it skews the results significantly towards the small population states and results in an even bigger discrepancy between the national popular vote and the final results. :-/

    Am I reading that right? I never knew that’s how it worked.

    1. Manan Shah Post author

      With respect to the comment:
      “HOWEVER, any penetration by third party candidates greatly decreases the likelihood of one candidate receiving a 270 majority …”

      I think what we see when that happens is that there is a vibrant third option that exists. Currently, third party candidates don’t make any dent in the electoral college directly, but rather indirectly, by apparently “sapping away” votes. Basically, third parties are viewed as parasitic and not a real political option.

      With respect to the “even worse skew” should we have to go towards tiebreak rules, there are a few things to mention. If we really go towards proportional electoral college, then we can probably reviist those tiebreak rules. Second, if we’re going to have a bias, I’d rather that bias be further downstream (tiebreak rules, eg) than from the get-go. It’s unclear how frequently those tiebreak rules would kick in if voter turnout actually increased materially.

      I haven’t done the exercise to see what happens in all elections. It’s an exercise in getting data properly organized … but maybe one day I will!

      1. AMH

        I agree that pushing the bias further downstream to the tie-break rules is more desirable than having it there in the current winner-take-all electoral scheme up front. And I don’t think the tie-breaker problem I’m talking about means that proportional electoral college ideas are wrong/bad/should not be pursued.

        I do think, however, that the tie-breaker rule as it stands could very likely tank the whole plan if we somehow got momentum behind the proportional idea. I haven’t run through exhaustive data either, but it looks like the tie-breaker is a MUCH more likely case in the proportional electoral method than in the current winner-takes-all. So any push for this should include a close study of the tie-breaker scenario, and how that could be changed (does it require an amendment? is there a way to ensure that the ONE vote from each state is cast in a proportional way? hmmm…)

        To be clear — I don’t take your response as negative or defensive in any way, and I hope I’m not coming across that way to you. I’m really enjoying the exchange of ideas. Thanks for your time and intellect applied to this issue!

        1. Manan Shah Post author

          Yeah, I agree that if we really do move to a proportional system, then that tie-break scenario ought to be revamped as well. How that happens within our legal framework is a bit outside my expertise, but I’m sure there’s a way.

          No offense or hostility taken in your response and there is none from me either! Communicating over a text-only medium can be challenging!

  4. Richard Fox

    All I see here is an immense amount of effort put into an attempt to torture the electoral college into a democratic outcome. The USA is not a democracy. It is a Republic. “For the people by the people” means all of the people, not just the mob. All this solution does is ensure mob rule. The electoral college is not proportional for a reason.

  5. Tys

    From Erica’s comment above: “If in 2016 no Trump Electors could bring themselves to listen to the news reports between 11/9 and 12/19 that showed him to be unfit for the office of president and change their votes, then no significant number of Electors ever will do so. (This election was our most compelling case of unfitness in the history of the U.S..) Therefore, that particular purpose of the Electoral College has been nullified by experience. It isn’t effective.”

    holy crap that’s a good argument.

    very good responses here to this very well put argument. yes, machine/math IS better, but the trust issue is also huge, and won’t allow the “black box” of computer math to be the decider.

    Even though we have the right solutions and we know the problem, and that it’s a big problem… one can see that without something else, nothing will change. what is that other thing? Political will? from whom? congress? pah.

  6. Erica Siskind

    I get that you are rounding down instead of rounding up or down as we normally would do because we are limited to a fixed number of electoral votes. However, it still presupposes that each Electoral College vote is a whole number because it is connected to a whole human being that will eventually cast the Electoral College ballot in December.

    But what if we disconnected it from a human being, who could (but apparently never actually would) change their vote? If in 2016 no Trump Electors could bring themselves to listen to the news reports between 11/9 and 12/19 that showed him to be unfit for the office of president and change their votes, then no significant number of Electors ever will do so. (This election was our most compelling case of unfitness in the history of the U.S..) Therefore, that particular purpose of the Electoral College has been nullified by experience. It isn’t effective.

    But people (especially Senators) may believe there are other compelling reasons to keep the set-up of the Electoral College, perhaps related to an intentionality of disproportionate representation by less populous states. Since we have a special interest in protecting the rights of minorities, it almost makes sense to me – but as a lifelong resident of California, it’s a stretch that I’m only indulging for the sake of argument.

    So, let’s say we keep the Electoral College, apply proportional representation, but take out the human Electors. Then we would see (in your example) that Trump would get 7.60, Clinton 7.56, and the various 3rd-party candidates would add up to .84 Electoral College votes – a total which is mathematically correct for the state. The Electoral College vote would be done by machine – in December, as currently scheduled, a reasonable time after the November election so that we could actually do a true audit of every state’s ballots, and a recount where/if necessary.

    It seems to me that mathematicians especially should get behind the necessity of always doing a nation-wide audit to make sure the numbers that are reported match the intentions of the voters. In fact, we voters should instantly receive printed receipts showing that the machines counted our ballots as we intended. With that evidence, we could create a level of trust in our elections that we have never yet fully achieved.

  7. David Griswold

    It doesn’t have anything to do with calculators. It has to do with states’ power. How the states apportion electoral votes is entirely up to them, and no state wants to water down its own power in the vote by going proportional (except that both Nebraska and Maine kind of do, voting by Congressional district).

    The only way to make this happen would be with a constitutional amendment, at which point why not just go with the popular vote? And neither will every happen because, again, states’ power.

    1. Manan Shah Post author

      I absolutely agree that changing the system is going to run up against each state’s sense of self-worth and influence. I’m thinking of a compromise between a pure popular vote [making states’ power effectively zero] vs the current system. If the argument is that no state wants to give up / water down its power, then a popular vote won’t happen, as you say. But if there is great clamor about the injustice of the existing system, then a reasonable compromise, if states are willing to compromise, would be a proportional electoral college.

      As it stands, most states’ influence is basically zero. And by that I mean, it is already known with near certainty which way the state will vote. Hence, that state’s ability to gain the attention of candidates is zero. It’s a waste of time and money for either candidate to try to garner more voters, say, California. As a consequence we have a hyper-focus on a handful of states [Michigan, Pennsylvania, Florida, eg].

      So, I would argue [with a little hand-waving] that we have, in effect, six or seven states that matter. All the other states make up a base for the two main party candidates. A popular vote system makes no states matter. A proportional electoral college gives some positive weight to all states in that there is an incentive for each candidate to acquire more votes, even if they lose the state since they have the ability to siphon off electoral votes.

      I suppose a counterargument to what I just said is that if the proportions in each state tend to be stable over time, then this system will reduce to those states where the proportions are more volatile. But the variance in the proportion is not obvious to me since every vote will matter. Will voter preference be more or less volatile if every vote mattered on a state-by-state basis?


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