See, I’ve seen all kinds of different definitions of “bayesian regret”.
There aren’t really multiple different definitions, at least as it pertains to social choice.
For example the ability to identify the original condorcet winner after noise has been added to the votes until there is no condorcet winner anymore.
That wouldn’t be a different definition of Bayesian regret, it would be a different social welfare function plugged into your regret calculations. But as I said, it’s mathematically proven that a majority/Condorcet winner is not necessarily the social utility maximizer. So Condorcet-ness is an irrelevant property. (And Score Voting and Approval Voting are plausibly better Condorcet methods than real Condorcet methods, in practice.)
I saw another paper where they used a game-theoretic approach and measured their results according to “voter happiness”.
Happiness, utility, satisfaction, etc. Whatever you want to call it. That is precisely the thing you want to measure. Decision-making is about maximizing utility, hence the reason natural selection gave us this grey decision-making machine between our ears, and endowed us with the notion of pleasure and pain and desire to begin with. An election is just a decision made by more than one entity, and is fundamentally the same.
Then there are the issues with cardinal methods like score voting. They’re subject to tactical voting like bullet voting and team bullet voting.
Absolutely false. The best strategy with Score Voting is not to bullet vote. Indeed, as I pointed out above, there is a theorem that even if 100% of voters are tactical, you end up with the Condorcet winner when there is one, which is actually a pretty good outcome in most cases. Here’s a page I wrote summarizing and linking to more than 20 of the best and most comprehensive analyses of tactical voting.
A voting system that encourages or requires tactical voting is not a good voting system.
This is a common fallacy addressed at the top of the summary page I just linked to, specifically illustrated with this useful graph.
It would be unreasonable to opt to use “Random Ballot” there and get worse outcomes just so we can say, “but there wasn’t any tactical voting”. What a rational individual wants to focus on is voter satisfaction given whatever amount of tactical voting may occur.
Not only that, but score voting doesn’t even guarantee constant voting power. If you give more than one candidate maximum score you effectively multiply your effect on the election. That can’t even be called democratic.
Not only is this incorrect, but the exact opposite is true, and this is the very reason the Equal Vote Coalition supports the Score Voting family of voting methods.
Simple example. Imagine there are three candidates and at the present moment it’s a tie. You vote for (give a max score to) candidate X. I have the exact opposite preferences that you have, so I vote for Y and Z. And then it’s still a tie! Our votes had opposite but equal effect, which is equality QED.
Virtually every ranked system fails this criterion, particularly Condorcet.