Twice now in recent memory, in the U.S. presidential election system, we have had the popular vote loser still win in the Electoral College. As laid out brilliantly in Lawrence Lessig’s recent blog post, *The Equal Protection argument against “winner take all” in the Electoral College*, the blame for this can be laid at the feet of the “winner take all” system of allocating electors used by the vast majority of states.

Within that post, a spreadsheet from Atlanta attorney Jerry L. Sims is shared that shows how the electors would have been allocated if each state had allocated them proportional to the popular vote. I was not happy with the methodology, though. They apply an arbitrary requirement of candidates needing a *de minimus* 5% of the vote in order to get allocated any electors. Looking at California, which has 55 electors, a *de minimus* 1.8% (~1/55), would have been a more appropriate choice. A 1.8% *de minimus* should have produced one elector for the Libertarian candidate (who received 2.6%). I suspect it is no accident that a 5% *de minimus* results in Clinton/Kaine receiving the requisite 270 electoral votes to win. I feel Lessig and Sims went against their own fairness arguments by pressing a thumb on the scales in favor of the two major parties.

In my recent blog post, Presidential Elections Efficiency Gap, I was inspired by the notion of the efficiency gap. The efficiency gap, as nicely explained and illustrated in the Washington Post, is a comparison measure of how fairly voters are represented in legislatures, based purely on votes cast in actual elections. The deeper notion in efficiency gap is that the representatives in an elected body should ideally be selected proportionally to how the populace votes.

Put in the language of the efficiency gap, the most fair representation result is one that minimizes the number of wasted votes, i.e, votes that didn’t ultimately get representation. To that end, I will attempt to lay out a scheme here that, like in the spreadsheet above, attempts to fairly and efficiently allocate electoral votes. In my scheme, I strive to not unnecessarily disenfranchise voters for third parties or independent candidates. I attempt to adhere to the following principles in my scheme:

- The number of people voting for electors in each state whose votes are “wasted” should be minimized, within reason.
- States independently select their electors, just once. That is, there can be no automatic run-offs or reallocations in the case that no candidate garners 270 electors. That would be adjusting the individual states’ results based on the national result.

Here is the scheme: For each state, define V as the total popular votes cast. Define V_{i} as the votes cast for electors for the i’th party/candidate, such that ∑V_{i}=V. E is the number of electoral votes allocated to that state. B_{i}=⌊E×V_{i}/V⌋ is the baseline number of electors allocated to the i’th candidate. R_{i}=V_{i}-⌈V×B_{i}/E⌉ is the remaining “unused” popular votes for the i’th candidate. The R_{i} all have the property that they are less than V/E. We now allocate the remaining electoral votes, E-∑B_{i},one at a time by sorting the R_{i} from largest to smallest. The end result is the E_{i}, the actual allocation of electors to the college. Taking my earlier California example, using data from the current Wikipedia page for the 2016 election:

Candidate | Popular Votes | Percentage | B_{i} |
R_{i} |
E_{i} |
---|---|---|---|---|---|

Hillary Clinton – DEM | 8,696,374 | 62.28% | 34 | 63,827 | 34 |

Donald Trump – GOP | 4,452,094 | 31.88% | 17 | 135,820 | 18 |

Gary Johnson – LIB | 474,615 | 3.40% | 1 | 220,715 | 2 |

Jill Stein – GRN | 275,823 | 1.98% | 1 | 21,924 | 1 |

Others | 65,507 | 0.47% | 0 | 65,507 | 0 |

Total | 13,964,413 | 53 (out of 55) | 55 |

How fair is this allocation? At one extreme, Jill Stein gets 1 elector for 1.98% votes cast. At the opposite extreme, Gary Johnson gets approximately one elector per 1.70% votes cast. The two major party candidates fall in the middle. Only “Other”, with just 0.47% of the cast votes, is unrepresented. This seems right, given that 1/E is about 1.8%. Contrast this with the earlier-cited spreadsheet, which with the above vote counts would have still allocated 35 electors to Clinton and 20 to Trump. That’s 1 elector per 1.77% of the popular vote for Clinton, and 1 elector per 1.62% of the popular vote for Trump. However, ~4.7% of the popular votes went unrepresented. I see this as 10 times more unfair than the 0.47% lack of representation in my scheme.

Using the same “townhall” dataset as I considered in my efficiency gap post, here’s the electoral vote tally I come up with:

Candidate | E_{i} |
---|---|

Hillary Clinton – DEM | 262 |

Donald Trump – GOP | 261 |

Gary Johnson – LIB | 13 |

Jill Stein – GRN | 2 |

Others | 0 |

Total | 538 |

The California result was identical to that given here considering the latest data, giving me confidence in the result’s robustness. The earlier dataset showed only a 47.0% of the national popular vote for Trump, while the latest Wikipedia data set shows only 46.1% Trump, with Clinton’s percentage holding essentially constant at 48%. It’s possible that might alter this result by switching as many as 4 electoral votes away from Trump to other candidates, but it doesn’t even come close to affecting the outcome. There are 2 major observations to make about this outcome:

- Most importantly, the almost 5.9 million (at latest count) votes cast for the Green and Libertarian candidates get some representation. Admittedly, Jill Stein got over 1% of the popular votes, which one would hope would have translated into about 5 electors, rather than 2. However, as I stated above, the idea in the Constitution that the
*states pick the electors*should be respected. Also, 2 electors is infinitely more representative than zero. - Both the major party candidates are denied the 270 electors needed for a win under the rules of the Electoral College. This outcome shouldn’t be surprising that when the popular vote is close and there’s a big desire for change, pushing many people to third party candidates. Having no Electoral College winner throws the election to the state delegations in the House. The vote would be among the top three Electoral College candidates (Clinton, Trump and Johnson). where it is likely that the Republican candidate would be selected by a vote of 27-24.

It could be argued that a Trump win in the House is itself disproportional, and due to gerrymandering distortion. However, it would still be a valid, legal result, ultimately determined by *state representatives*. It is up to the courts to solve the gerrymandering issue.

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