It’s the same problem the country faces every ten years when it divides 435 House seats among 50 states. A state’s fair share almost never comes out to a whole number, so a rule has to decide who gets the leftovers. Different rules give different answers, and people have argued about them since George Washington’s first term.
One example, four answers
Take a toy state with 5 electors and 100 votes: A 49, B 32, C 19. One elector’s worth is 20 votes, so C falls just short. For the ranked-ballot method, assume C’s voters all rank B second. Each method below gets a different result from the same votes.
| Method | A | B | C |
|---|---|---|---|
| Largest remainder | 2 | 2 | 1 |
| Threshold | 3 | 2 | 0 |
| Threshold with ranked ballots | 2 | 3 | 0 |
| D’Hondt (Jefferson’s method) | 3 | 1 | 1 |
Largest remainder
This is the method Fair Slate uses on the main page. Each candidate gets the whole-number part of their share, and any electors left over go to the largest fractions. It’s the easiest to explain: anyone can check it with a calculator.
Figure 11, step by step: Largest remainder
It’s also the oldest idea on this page. Alexander Hamilton devised it in 1792 for apportioning the House, and it’s still known as Hamilton’s method. The House used it from 1850 to 1900, until it ran into the “Alabama paradox,” in which a state could receive fewer representatives if the House got bigger. For electors, the number per state is fixed by the census, so that particular paradox doesn’t arise within a single election, but it shows why mathematicians are wary of the method.
Note what happens to C. With 19 votes, less than one elector’s worth, C still wins an elector on its large leftover fraction. Some see that as a feature (every sizable group gets a voice) and some as a flaw. The next two methods are ways to prevent it.
Threshold
Drop any candidate who falls short of one full elector’s worth of votes, then split the electors among the rest. It needs no new ballots, and it keeps electors from going to candidates who never earned a full one.
Figure 12, step by step: Threshold
The issue is in the result line: C’s 19 voters elect no one, a small version of the winner-take-all problem. And when the remaining candidates are nearly tied, the margin between them starts to matter again. On real data, a threshold would have cut 2016’s third-party electors from 16 to 5, and decided Florida 2000’s last elector by a few hundred votes (see the main page).
Threshold with ranked ballots
The same cutoff, but voters rank their choices. When a candidate is dropped, their votes move to each voter’s next choice instead of being discarded. Australia elects its Senate this way, statewide, with voters ranking parties.
Figure 13, step by step: Threshold with ranked ballots
Here C’s voters change the outcome: their second choice, B, wins the extra elector. It’s arguably the fairest of the four, and also the biggest change, since it requires new ballots and a longer count (more on ranked ballots).
D’Hondt, or Jefferson’s method
Divisor methods work differently. Instead of rounding shares, they divide each candidate’s votes by a series of numbers and hand out electors one at a time to the highest results. In D’Hondt’s version, the divisors are 1, 2, 3, and so on: a candidate who has already won electors has their total divided down, so each next elector is harder to win.
Figure 14, step by step: D’Hondt, or Jefferson’s method
This one has history too. In 1792, Washington used his first veto on an apportionment bill, and ten days later Congress adopted a method Thomas Jefferson had described, later known as Jefferson’s method. It’s the same as the D’Hondt method many countries use today, and it apportioned the House from 1790 to 1830. Since 1940 the House has used another divisor method, the method of equal proportions.
D’Hondt tends to favor larger candidates, which is why A wins a third elector here. Other divisor methods, like Webster’s, use different divisors and treat large and small candidates more evenly. In this example, Webster’s method happens to match one of the results above.
Which is best?
Among specialists, divisor methods usually win. As Wikipedia’s summary of the field puts it, “the divisor methods are generally preferred by social choice theorists and mathematicians to the largest remainder methods, as they produce more-proportional results by most metrics and are less susceptible to apportionment paradoxes.” (source)
But a method also has to survive contact with the public, and that favors the simple ones. A voter can check largest remainder on a napkin. Divisor methods and ranked-ballot counts take more explaining, and reforms that are hard to explain are easy to attack. Ranked-choice voting itself shows the risk: Burlington, Vermont repealed it in 2010, 52% to 48%, after a contested mayoral race, and Alaska’s 2024 measure to repeal its system failed by just 664 votes.
That’s why the main page uses largest remainder: it’s transparent, close to the vote, and easy to defend. But any of these methods is far more representative than winner-take-all, and a state could reasonably choose any of them. The model bill text leaves the method as a blank for exactly that reason.