Voting is important in cases where multiple criteria need to be optimally fused into a single decision.
The above link came from page talking about Arrow's Impossibility Theorem: https://mises.org/wire/arrows-impossibility-theorem-exposes-...
... I'm not that happy with the scary tone of the article but the summary of the theorem is a useful start for what follows...
Interestingly, the IIA result (Arrow's postulate 3, on that page), was shown experimentally by Khaneman and discussed in _The Undoing Project_ to be a irrational behavior experimentally exhibited by humans making a decision. In this experiment prisoner's were asked to choose between food items and then a third, irrelevant food choice, was offered. Non-transitive choices would appear in a significant fraction of the prisoners.
Reading the Mises.org article reminds me why humans might change their decision given irrelevant information (Arrow postulate 3). Breaking Arrow postulate 3 might be necessitated by using a voting algorithm that prefers being anti-dictatorial (Arrow postulate 1) and assuring that any globally preferred choice is selected over any globally less-preferred choice (Arrow postulate 2). Y
It has been shown that a voting scheme can preserve Arrow postulates 1 and 2 only if one allows irrelevant choices to change voting behavior (e.g. strategic voting in our current first-past-the-post, plurality, voting system).
Please consider Borda Count which is said to be close to optimal but still can be 'gamed' by strategic collusive voting. See: https://en.wikipedia.org/wiki/Borda_count
Also please consider Ranked Choice. In ranked choice there are rare cases where globally preferred choice lose to a globally less-preferred choice (Arrow postulate 2). See: https://en.wikipedia.org/wiki/Ranked_voting
Interestingly, Ranked Choice tends to retain incumbents in popular elections because name-recognition tends to produce many valuable runner-up votes. This is why some think a certain Senator from Maine survives challenges by well-funded opponents.