Today, we're going to repudiate Reader McStrawman's claim that Arrow's impossibility theorem shows that there is no "best" voting system.

This theorem is often invoked in a pessimistic way to shut down someone presenting an alternative voting system. My thesis here is that this statement is wrong, and harmful to public discourse.¹

REVIEW: Arrow's theorem proves that, if voters rank their candidates, there is no system that satisfies these three criteria:

• If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
• If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).
• There is no "dictator": no single voter possesses the power to always determine the group's preference.

Even though no rank order voting system can always satisfy these criteria, this doesn't say anything about how badly or frequently these criteria are broken.

Thus, you can do better than lateral movement between rank voting systems. Indeed you can improve upon outcomes between rank-based voting systems depending on the candidates and the preferences of the population (depending on how you would measure "success"). From the horse's mouth:

I think the answer is you have to ask, in effect, which ones get closest to this combination? And we have to then begin to look at what actual votes are. The real we do it is to apply some rule and to take elections and apply different methods and see what violates these conditions as little as possible. Remember all we’re saying is there could be a set of. We’re not saying you’re always getting a violation of these rules. We’re just saying there can be preferences of individuals which will cause one rule or the other to be violated. It may be the preferences of individuals which cause violations to occur very infrequently.

Moreover, this theorem says nothing at all about cardinality of preferences; the theorem is entirely within the realm of preference rankings. For example, assume that Reader McStrawman's preferences over purely hypothetical candidates are as follows:

He would be content with candidate HC
He would not be too happy with, but accept candidate GJ
He abhors the thought of candidates DT and JS winning

Thus, his ordering would be HC>GJ>DT~JS. But this doesn't reflect additional the information that he would consider the utility in [0, 100] space of each candidate being elected as follows:

HC: 90
GJ: 65
DT: 0
JS: 0

Thus, a voting system that captures this additional information (ex: "score your preference for each of the following candidates on a scale 1-5") is not subject to the impossibility theorem.

Insisting upon the impossibility theorem as a result that invalidates possible improvement between the outcomes of voting systems is harmful, because whether improvements are possible is ultimately an empirical question and a question of metrics used to measure satisfaction of the system.

Considering how little movement there has been within voting systems in the last half century, and the importance of the outcomes, harming public discourse is a Very Bad Thing^TM.

I rest my case.

1: A side goal of this post is to show to statist mods that purely theoretical RIs are suitable ^{andStageAPopulistCoup}