[caf]

The non-monotonicity tactical voting possibility is overblown: it only really works in the toy "which is the favourite pizza of these 30 students" examples.

In real world elections, the conditions where it is even theoretically possible arise only rarely (A > B > C with three choices, but B > A and A > C with two choices, and A's lead over B significantly greater than B's lead over C in the three choice scenario, and A's lead over C in the two choice scenario more than twice B's lead over C in the three choice scenario) and more importantly, they're not predictable enough beforehand. Advocating this kind of tactical vote stands at least as much chance of hurting your candidate as helping them, so nobody does it.

When you analyse real-world large scale IRV elections, you find that cases where the IRV winner isn't the Condorcet winner are rare, and this balances against the very real benefit of having a counting method that is easy to explain and understand.

[godelski]

The non-monotonicity is actually pretty important and we have real world examples of this. Clay mentions the Alaska race in this comment[0]. We've seen this issue in Southern states that used this to disadvantage black voters. This is also the reason Bernie would spoil Biden (and vise versa). So I'm not sure what you're getting at.

[0] https://news.ycombinator.com/item?id=27598975

[caf]

Let's look at the "Bernie would spoil Biden" example.

The idea is that the Republicans endorse only one candidate, Trump, and the Democrats endorse two: Bernie and Biden. In the non-tactical voting case, the second-last round votes shake out like:

  Trump 45
  Biden 28
  Bernie 27

Bernie is eliminated, the votes in his pile split 24 / 3 between Biden and Trump (a preference flow of 89% to Biden) and the final round of counting ends up:

  Biden 52%
  Trump 48%

..but tactical voting intervenes! A small number of Trump voters (2% of the total electorate) are organised to tactically switch their votes to 1. Bernie 2. Trump, resulting in a second-last round of:

  Trump 43
  Bernie 29
  Biden 28

Now Biden is eliminated, the votes in his pile split 20 / 8 Bernie/Trump (a weaker preference flow of 71% to Bernie, because of Biden voters too conservative to vote for Bernie) and the final round is now:

  Trump 51
  Bernie 49

Tactical voting has won the day!

However, this really illustrates the problems here for the prospective tactical voter:

1. They need pretty perfect information to pull this off. Not just on first round votes, but on how the preferences are going to flow as well. If those Biden votes flowed a little weaker to Trump, all they'd have done is elect Bernie instead; if Trump had been a little stronger overall than they expected in the no-tactical-voting, their tactical voting attempt might have backfired completely and turned a fair Trump win into a loss! Opinion polling just isn't this precise.

2. They have a co-ordination problem. If they switch too few votes, the scheme fails and they just elect Biden with a greater margin than before; too many and the scheme fails and they elect Bernie, a candidate they're presumably less happy with actually getting the Presidency than Biden.

3. All of this only works if the balls line up perfectly in the first place, even setting aside the problem already mentioned of how you know the balls are going to line up. If the second-last round votes are instead Trump 45 / Biden 30 / Bernie 25 then the Bernie to Biden preference flow has to fall under 66% for the scheme to be possible.

Rather than trying to engage in this dubious and risky tactical voting attempt, the Trump campaign would be far better served just spending their resources trying to turn out more of their voters. After all, the theoretical possibility only exists when the margins are tight in the first place.

A tangential matter is that even in an IRV election it still probably makes sense for the parties to either endorse only a single candidate each - otherwise their candidates will waste some of their resources attacking their co-party candidate when they could have launched them against their main opposition - or at least mutually agree to distribute campaigning material advising to give a second preference to their co-party candidate (a so-called "preference swap" arrangement).