What’s the Matter with Iowa

This was initially published yesterday as part of Prelude to Iowa. It looks like this scenario is playing out in real time so it deserves to be out on its own.

Beware of Paradoxical Results

You might think that first-past-the-post or the plurality vote is the worst voting system ever. You’d be wrong. In 2017, my student, Brandon Payne studied the Iowa Caucuses. He determined that the caucuses violate all sorts of mathematical “fairness criteria.” One example is the Condorcet criterion which states that if one candidate beats every other candidate in head-to-head match-ups, that candidate should be the overall winner. Such a candidate might not win the Iowa Caucuses.

Turns out, the viability constraint can also lead to seemingly contradictory results, which I’ll call the “viability paradox.” As a quick example, suppose that in some state, the voters have the following preferences.

Candidate A35%
Candidate B30%
Candidate C12%
Candidate D12%
Candidate E11%

In a primary election, this would be a clear victory for candidate A.

Now let’s divide our state into five precincts of 100 voters each and let’s assign each precinct 10 delegates. We’ll conduct a caucus to allocate the delegates.

Suppose that the voters are arranged within the caucuses according to the graphic below.

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Notice that there are non-viable candidate preference groups in each precinct. These voters will have to join a viable group in order to participate. They may reorganize themselves as shown below.

This image has an empty alt attribute; its file name is image-1.png

And so, in this case, Candidate B actually wins pretty decisively, probably 23 delegates to 15 delegates for A. Candidates C, D and E should get 4 delegates each.

There might be good reasons to decide that either candidate A or B is the rightful winner here, but one point is that there is a significant difference. Systems like this can lead to chaotic or paradoxical results. One important take away is that, right or wrong, geography can have a lot of influence on who the victor will be. Even if a candidate seems to be ahead in the polls, they can lose without any shenanigans going on, simply because how their voters are distributed across the state. Surprising results aren’t necessarily nefarious or even necessarily surprising.

You might even want to argue that results like this are a good thing because a lot of voters got to express their second choices. Here’s why you’d be wrong. It’s not systematic. In Instant Run-Off voting, for example, everybody’s second choice is counted unless their first choice is. In the caucus exactly whose second choices are counted is determined by an accident of geography. In deciding a winner between candidates A and B above, should the second choices of voters who picked candidate C in precinct 1 be less important than those in precinct 3? They shouldn’t be but in the current system they are. This is worse than a plurality vote because this could be taking us even farther away from a good collective decision.

In fact, it’s a bit worse than that. Apparently, the state weighs the delegate counts in rural counties a bit more heavily than their urban counties. If the Democrats who think we should dump the Electoral College are to have any intellectual consistency, they should reject these results and work to reform this process.


  • Payne, B., The Iowa Democratic Caucuses: A Mathematical Analysis of the “Vote,” Unpublished Manuscript.

How would presidential elections change if electoral votes were allocated by congressional district ?

First published on Quora.

This is the system currently used in Maine and Nebraska. In Maine and Nebraska the statewide winner gets the two electoral votes (EVs) that correspond to the senators and then the remaining votes are determined by the winner of each congressional district.

The Electoral College already has a “small state bias” that skews for the time being in favor of the Republicans, since the smaller states tend to be more Republican than the country as a whole. I haven’t checked the numbers, but California has the same population as something like the smallest 20 states combined. That’s two EVs for the statewide win in California compared to forty for the statewide wins in these other states. It’s this bias that is responsible for the two “electoral inversions” we had in 2000 and 2016. That is to say, the two elections where the winner of the Electoral College did not match the winner of the popular vote.

Choosing the remaining EVs by congressional district would further skew things in the Republican direction. This is due to the extreme partisan gerrymander that took place after the 2010 election. To put this into perspective, the Democrats won the “national congressional vote” (NCV) in 2018 by something around 7 percentage points. This will give them a majority of between 14 and 19 seats when the remaining races are determined. By contrast, the Republicans won the 2014 NCV by 5.4 percent in 2014 and that gave them a majority of 30 seats. Worse, in 2012 the Democrats won the NCV by 1.2% but the Republicans maintained a majority in the House of 16 seats.

So, at least until the the congressional districts are redrawn in the wake of the 2020 Census, the current small state bias that favors republicans would be exacerbated. I don’t know if it would be impossible for a Democrat to win the presidency under such a system, but it would certainly be more difficult and there would be many instances where this system would elect the Republican even if the American people preferred the Democrat.

Still, it’s easy to imagine a worse system. During the run-up to the 2012 election, I recall Nebraska debating a return to a winner-take-all system so that President Obama could not win an EV from Nebraska like he did in 2008. At at about the same time the republican-controlled Pennsylvania legislature debated switching to allocating EVs by congressional district to help Governor Romney. Imagine such a system implemented nationwide, with all the red states using winner-take-all and all the blue states allocating by congressional district or vice-versa. Such a system would virtually guarantee one-party control of the presidency.

References (all accessed 19 November 2018):

House Election Results: Democrats Take Control

RealClearPolitics – Election Other – 2014 Generic Congressional Vote

RealClearPolitics – Election Other – 2012 Generic Congressional Vote

114th United States Congress – Wikipedia

113th United States Congress – Ballotpedia