What about kicking candidates off the island?
An exhaustive ballot.
It has problems too. At 90% elimination the run-offs would be quick. Assuming 100,000,000 candidates:
100000000
10000000
1000000
100000
10000
1000
100
You could spread that out and have say 1 election every 2 months. Or if you wanted it weekly, you'd need to eliminate only about 25% each round:
100000000
75000000
56250000
42187500
31640625
23730469
17797852
13348389
10011292
7508469
5631352
4223514
3167635
2375726
1781794
1336345
1002259
751694
563770
422827
317120
237840
178380
133785
100339
75254
56440
42330
31747
23810
17857
13393
10045
7534
5650
4237
3178
2383
1787
1340
1005
754
565
424
318
238
178
133
100
75
56
42
That doesn't seem reasonable. Nearly half the elections have over 100,000 candidates running, which is going to be confusing. Did my preferred candidate get eliminated last week? I better hope I have internet access and I had also better hope I have legible hand writing cos it'd have to be a write in vote, which slows counting considerably.
But even in theory...
It falls prey to what I think of as the 'Weakest Link' problem:
Sanders: 25 million votes
Clinton: 30
Trump: 45
No winner, Sanders is eliminated, Clinton gets their votes next round:
Clinton: 55
Trump: 45
Clinton wins.
But let's say some of the Trump supporters voted for Sanders in the first round:
Sanders: 31 million votes
Clinton: 30
Trump: 39
Now Clinton is eliminated. Given the 6 million Trump supporters that voted tactically last round will now vote for Trump that means Trump is more or less assured 45 million votes. It'd only take another 6 million Clinton supporters to vote for Trump over Sanders to give the election to Trump.
Obviously, voters can't know how other people are voting, so its risky, but it is a time-smeared version of the problems in other run-off type elections (with the added issue of unstable voter preferences - they change over time). This issue obviously already exists therefore in the primaries. Your version takes longer, and *may* result in some better candidates. However,
No parties
The system creates parties, you can't assert them away.
Let's consider 100 candidates all with equal amount of the electorate, except one candidate has a little more than 1% of the vote and another has a little less. If I'm eliminated, the people that support me are going to look to me for suggestions of alternates, people I think have similar policies or ideas. That is, an endorsement is a powerful tool. This means agreements are inevitably going to arise, coalitions will form and parties will follow. It's as inevitable as the problems in communism, human nature won't allow it regardless of high-minded ideals.
Should be the one most can live with?
Honestly, you get basically the same effect as with Instant Run-off voting, but smeared over time such that global or local events can change people's minds just as much as communicating policy, meaning the mandate is 'smeary' and difficult to completely claim. Maybe someone who is eliminated one week ends up doing or saying something so amazing that suddenly 60% want that person as President and now everyone thinks the rest are just 'meh', which harms the power of the incoming President.
Having people that don't even want to run seems like a waste of time. I expect that given a few rounds and the top 10 candidates will be fairly stable, with the top 2 being consistently in the top 2. If we simply eliminate all people that receive 0 votes in any round, that might make the whole process a little more sane.
Of course, the optimum strategy might be to vote for yourself until you are eliminated, and if enough people followed this we're back to a bit of a grind in the eliminations.
Should be the one most can live with?
I mean you could do the same thing with a GIGANTIC ballot and IRV if we're just sticking to theory and ignoring the practical problem with this:
"I just voted"
"Cool, how long did it take"
"I only ranked 100,000 of the candidates so it took me a mere 2 months"
In short, while I think having more candidates available and some kind of preference selecting run-off is likely the best way forwards, the 'add more candidates' tactic gives us diminishing returns.
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