To the reader: approval / score voting has its own problems, such as not satisfying the majority criterion (a bigger deal than monotonicity) and encouraging strategic voting, among other problems.
IRV actually encourages strategic voting, see e.g. http://mattbruenig.com/2014/11/15/instant-runoff-voting-and-.... For a concrete example, if in the USA we had an IRV election between Trump, Clinton, and Sanders in 2016, there are some (not unrealistic) scenarios where it's possible that your (honest) choice to vote 1. Sanders 2. Clinton 3. Trump would cause a Trump victory, whereas a strategic vote of 1. Clinton 2. Sanders 3. Trump would cause a Clinton victory.
You can argue that approval voting also can lead to strategic voting, but at least with approval voting you won't accidentally cause your least favorite candidate to win by voting honestly.
You should look at Condorcet methods, which as a group are conceptually similar to IRV but are more effective at capturing the intent of the electorate. For example, the above scenario can't happen with Condorcet methods. (Again the problem there is that there are actually many of them, and you have to agree on which specific one you want. But all are better than IRV).
IRV isn't the way forward, and it's unclear to me why organizations like FairVote don't endorse another method. (They have an article about it here but the reasoning doesn't really make sense to me. http://www.fairvote.org/why-the-condorcet-criterion-is-less-...)
Bucklin Voting's issue is that it can elect the candidate that is everyone's last choice.
There are ten candidates. Candidate J is least liked by everyone. Nobody else has a majority until the final preference votes are counted. At that time, the entries are tremendously skewed towards Candidate J, and he wins with the clear majority.
That doesn't apply. It is important to filter out voting systems that degenerate into the opposite of their goals. I don't understand why you say that is a mistake. This has nothing to do with a comparison but removing a poor voting system that does not meet the criteria.
At one time, two dozen US cities used STV, and at another time nearly two dozen used Bucklin. And all of them but Cambridge (STV) reverted to Plurality.
So it's just tough, because people are tough.
There's some truth to the statement about IRV. If people are strategic, it essentially degrades to Plurality Voting. http://scorevoting.net/TarrIrv.html
That's not to say that 100% of voters actually are strategic with IRV, but strategic voting appears to have caused IRV to maintain duopoly in countries like Australia—which is pretty undesirable IMO. http://scorevoting.net/AustralianPol.html
Interestingly, polls show that a majority of Australians want to replace STV/IRV with Plurality. http://scorevoting.net/WhatVotersWant
As for these specific criteria, let's be clear from the start that criteria are a very dumb way to assess voting methods, kind of like comparing race cars by comparing horsepower and drag instead of just putting them through timed trials. http://scorevoting.net/PropDiatribe.html
The answer there is Bayesian Regret, which shows Approval Voting performing exceptionally well, and IRV doing worst of the five commonly discussed alternatives. http://scorevoting.net/BayRegsFig.html
Non-monotonicity is an actual problem—it results in a mathematical proof that the voting system has elected the wrong candidate in at least one of two "mirror image" scenarios.
Failing the majority criterion is NOT a problem, in a technical mathematical sense. One of the most elementary facts of social choice theory is that it's possible for a group to prefer X over Y even though a majority of its members prefer Y to X. Mathematical proof here:
http://scorevoting.net/XYvote.html http://scorevoting.net/CondorcetCycles
Though for practical purposes this is all irrelevant, as it would be astronomically unlikely for a majority-preferred candidate to lose with Approval Voting. There is even a theorem that Approval Voting will elect Condorcet winners under rational voter strategy.
With a good voting system, we'd expect/hope to see a competitive race with many candidates, so even having a majority favorite would be the real problem. Without that, the concept of a "majority winner" is nonsensical, yet you still see IRV proponents touting their system's ability to "guarantee a majority winner". I profile the absurdity of this claim here.
https://sites.google.com/a/electology.org/www/utilitarian-ma...
Instant-runoff voting can punish voters for prioritizing a 3rd party candidate. IRV does not satisfy the monotonicity criterion. See this article [1] for more information.
In general, IRV is a poor system that is almost as bad as plurality voting in terms of how the outcomes reflect the voters' preferences (plurality voting is what the United States uses for most elections).
There are many systems that are better than IRV or plurality. I like approval voting [2], which is a system where you can vote for any number of candidates (instead of one candidate like plurality). Unlike IRV, you don't rank your choices. Approval voting is very simple (the simplest option other than plurality) and produces good outcomes.
[1] https://en.wikipedia.org/wiki/Monotonicity_criterion [2] https://en.wikipedia.org/wiki/Approval_voting