samedi 12 novembre 2016

How tweaking the voting system would have impacted the 2016 election

The United States' system to elect the president seems to be quite unusual, and quite subject to debate, as this year the president winning the election did not win the popular vote.

Here I'll focus on a few of this system's characteristics, and how changing some of them would have impacted the results of the 2016 presidential election.

The point of this post is not to evaluate whether the system is good or not, not to advocate alternate voting systems, and not to promote any particular candidate.  It's just a boring analysis of numbers.

A few probably unique characteristics of the US voting system to elect the president are:
  • Voting for electors: A citizen does not vote directly for the president/vice-president ticket.  Instead, the citizen votes for an elector, a member of the United States electoral college, who has pledged to vote for that president/vice-president ticket.  Cases of electors not voting for the expected candidate are extremely rare.  Some states legally bind the electors to vote for their given party.
  • Electoral college vote distribution: Each state has a number of electoral college votes, which are distributed partially based on population, as positions in Congress are apportioned: a total of 538 votes are distributed.  First, 102 votes are distributed evenly to each state plus the District of Columbia (2 per state/DC), and the remaining 436 votes are distributed to the 50 states plus DC, based on population. 
  • Winner-take-all: Finally, most states (all except for Maine and Nebraska) have a winner-take-all system.  The candidate who wins the largest portion of the popular vote in a given state receives all of the electoral college votes of that state.
After seeing the results of the 2016 elections, with conflicting outcomes between the popular vote and the current system, and witnessing discussions about alternate voting systems, I was curious to see how changing any of these characteristics would have impacted the election.  My goal was to complete this table:

Elector loyalty Congressional apportionment of votes Winner-take-all Winner?
Current system: Trump 306 vs Clinton 232
Popular vote: Clinton 47.7% vs Trump 47.4%

I used the data reported on politico for my analysis. As of the writing of this post, politico is reporting 290 electoral votes for Trump and 228 for Clinton, with New Hampshire (4, Clinton) and Michigan (16, Trump) as not finalized yet.  I consider these counts final just to simplify my analysis, hence the result of 306 to 232 in favor of Trump just above.

Elector loyalty

What if the electors weren't bound to vote for their party?  They will vote on December 19, so there is still time to find out!  In order to change the election outcome (to not guarantee a Trump presidency), 36 Republican electors would have to not vote for Trump in December.  That's 11.7% of the Republican electors. Is it likely or even possible?  I'm not in a gambling mood right now.  We'll see.

Apportionment of votes

What if we kept elector loyalty and the winner-take-all system, but distributed votes based purely on population?  Specifically, what if 436 votes were apportioned to the 50 states plus DC based on population?

To find the answer, I wrote a Python script to extract the data from politico in HTML format and to save it to an Excel file.  I calculated the following and saved my analysis for this blog into a new file.
  • Determined the number of "population-based electoral votes" for each state simply by subtracting 2 from the "total electoral votes" for each state.
  • Assigned all the "population-based electoral votes" to the candidate who got the highest percentage of the popular vote, in each state.
  • Tallied the "population-based electoral votes" for each candidate.
The result is: out of 436 total votes, Trump would receive 245 votes, and Clinton would receive 191.  No third party candidate would receive any electoral votes in this scenario.  Trump still wins in this scenario, but by a wider or narrower margin?

In this scenario, Trump is ahead by 54 votes, compared to the real scenario, where he is ahead by 74 votes (306 - 232).  But, since there are fewer votes to distribute, we can't compare the two gaps directly.  We can compare percentage of electoral college votes:
  • Congressional apportionment: 306/538 vs 232/538 is: Trump 56.9%, Clinton 43.1%
  • Population-based distribution: 245/436 vs 191/436 is: Trump 56.2%, Clinton 43.8%
Using a population-based distribution of votes instead of a congressional distribution of votes would have almost no impact on the result of this election.


What if we kept elector loyalty and the congressional apportionment of votes, but abolished the winner-take-all system?  How would the electoral votes for a given state be distributed, based on the popular vote?

This turned out to be a tricky question.  In Maine and Nebraska, in the current system, each district has one electoral vote, and that vote goes to the candidate winning the popular vote in the district.  The remaining 2 votes for each state are given to the state-wide winner.  Nebraska, for example, has a total of 5 votes: 3 votes apportioned to 3 districts based on population, plus 2 other votes. If Nebraska has a candidate A win one district, and B win the two other districts, the likely outcome will be 1 vote for A and 4 votes for B.

I didn't have data for each district for the 50 states, so I couldn't do an analysis on this method on a nation-wide level.  Maybe I'll do a follow-up if I can obtain this data at some point... maybe not...

So how do you go about distributing votes in one state if you don't have data per district?  We can attempt to divvy up our allocated electoral college votes to the candidates based on their popular vote share. Let's take one state as an example: California.

D. Trump H. Clinton G. Johnson J. Stein Other Total
Votes 3,021,095 5,589,936 288,310 155,706 38,880 9,093,927
Percent votes 33.22% 61.47% 3.17% 1.71% 0.43% 100.00%
Electoral votes 18.3 33.8 1.7 0.9 0.2 55
Electoral votes (rounded) 18 34 2 1 0 55

In California, we see an interesting distribution with a couple of third parties getting some electoral votes.

However, in West Virginia, we have a rounding problem:

D. Trump H. Clinton G. Johnson J. Stein Other Total
Votes 486,198 187,457 22,798 8,000 3,773 708,226
Percent votes 68.65% 26.47% 3.22% 1.13% 0.53% 100.00%
Electoral votes 3.4 1.3 0.2 0.1 0.0 5
Electoral votes (rounded) 3 1 0 0 0 4

After rounding the fractional electoral votes each candidate should receive based on his share of the popular vote, we see that we've only allocated 4 of the 5 electoral votes for the state.  What do we do with the last vote?  I couldn't find a solution for this that would grant whole votes to candidates, with a nice formula in my Excel file.  So, I decided to just not round.  In this scenario, we assume that the electors are loyal anyway, so we don't really need them to be humans.  We can just replace them with "points", which can be fractional.

In this scenario, the results are quite different from the real-life scenario.  Here are the fractional electoral college votes allocated to the candidates:

D. Trump H. Clinton G. Johnson J. Stein Other Total
Electoral votes 253.4 257.0 18.0 5.5 4.1 538.0
Percent electoral votes 47.1% 47.8% 3.3% 1.0% 0.8% 100.0%
Percent popular vote 47.4% 47.7% 3.3% 1.0% 0.6% 100.0%

Without the winner-take-all system, Clinton is ahead by 3.6 votes, with 27.6 electoral votes being allocated to third parties.  The share of electoral votes is nearly identical to the share of the popular vote.  Any difference between the percent electoral votes and the percent popular vote is due to the congressional apportionment of votes, which we saw earlier, seems to behave about the same as a distribution based only on population.

The Excel file containing these calculation experiments can be downloaded here.



I'm finally able to fill out my table:

Elector loyalty Congressional apportionment of votes Winner-take-all Winner?
Current system: Trump 306 vs Clinton 232
Popular vote: Clinton 47.7% vs Trump 47.4%
Let's see in December
Trump 245 vs Clinton 191
Clinton 257 vs Trump 253.4

The attribute of our current system which appears most responsible for the difference between the popular vote and the election result is the winner-take-all rule.  The allocation of votes based only partly on population behaves closely enough to a distribution based only on population.

While I'm happy to have some answers, I don't believe I can conclude that if we had a system without winner-take-all, that the result would have actually been a 257-253 win for Clinton.  Voters' behaviors may change if we eliminated this part of our voting system, perhaps being more willing to vote for third-party candidates.