# Is there a name for this method of allocating electors? (Iterated rounding?)

Instead of eliminating the electoral college, one might shift it from a winner take all approach that most states use and mandate instead some form of proportional allocation of votes. Here is one idea for how proportionality could be implemented. Take the original vote counts for a position and normalize the votes so that they sum to 1. Round each normalized vote to the nearest 1/n where n is the number of electors in a state. Call this result Stage 1. The new normalization may or may not sum to 1 due to rounding error. But if we now normalize Stage 1 and keep iterating, sooner or later it appears that the total always comes out to 1.

Example: Vote counts are {734, 227, 1741} and 7 electors. On the first round, this reduces to {2/7, 1/7, 5/7}. On the second round this reduces to {2/7, 1/7, 4/7}. The result is now stable.

So my question is: (1) is there an existing name for this method; (2) does any known electoral system use it to map vote counts into representation?

• Does it always stabilize? Assuming usual rounding rules, I think [1,1,2] with three electors would cycle. 2/4 rounds up to 2/3 every time, while 1/4 goes to 1/3. – Geobits Nov 15 '16 at 16:36
• Same goes for [1,1] with three electors, for that matter. This case would be fairly common with a (mainly) two-party system where nobody receives an absolute majority. – Geobits Nov 15 '16 at 16:42
• Uh oh. I did not consider ties. I used random numbers to test it out and it always stabilized. I conjectured that this would always be the case but you have found counterexamples. – mathlawguy Nov 15 '16 at 17:32
• There are lots of proportional representation systems in use. There seems to be scholarship around how to determine proportionality: en.wikipedia.org/wiki/… – Jacktose Nov 15 '16 at 21:23
• This would not change the fact that an alaskan or north Dakotan vote counts way more than a californian vote. This seems to be the main critic the electoral college recieves. The "winner takes all " is applied at the end anyway in a presidential regime – user5751924 Dec 23 '16 at 17:35