Time for a math refresher. Let's shoot some arrows through the heart of democracy. From the quiver of Kenneth! A nobel man if ever there was! Stop changing "nobel," you annoying spell-checker! I meant to make it both -el and lower case.
Kenneth Arrow. Winner of the... oh, you get it. And yes, the Economics prize is real. He won the prize for his proof of the "impossibility theorem," which essentially states that there is no mathematical way to aggregate the preferences of a group of people over a number of choices more than two. So, the Democrats started the 2020 nomination contest with somewhere on the order of 165,000,000 candidates. This is only a rough estimate because it has always been in an indeterminate state, but I am simply taking the 50/50 split of the country, with a population of roughly 330,000,000, and to a first approximation, treating every Democrat in the country as a candidate, hence all of the craziness of who gets on stage.
And as silly as that sounds, there is actually a set of game-theoretic models called "citizen-candidate" models where literally everyone in the polity is treated as a potential candidate, and the whole game is about which people in the enormous polity enter the race in the end, and which ones don't. (Besley & Coate, Osborne & Slivinski are the main cites here, and yeah, I actually need to cite this stuff when I write formally.)
Back to Kenny, though. You know he's dead, right? Bastards... Anywho, with more than two choices to consider, you might rank the choices as Candidate A, then B, then C. Another voter might prefer B, then C, then A. Another might prefer B, then A, then C, and so on.
Arrow was concerned with whether or not you could take a group of people, and how they "ranked" the options, and then convert that into a single ranking for the electorate of all the choices. His conclusion, via rigorous proof? You can't, once you get more than two choices. It's impossible. Hence, the name of the theorem. Simple demonstration. Suppose Voter 1 prefers Biden to Warren, then Sanders. Voter 2 prefers Warren, then Sanders, then Biden. Voter 3 prefers Sanders, then Biden, then Warren.
A majority of this group (1 and 3) prefer Biden to Warren. A majority of this group (1 and 2) prefer Warren to Sanders, and a majority of this group (2 and 3) prefer Sanders to Biden. Got that? A majority prefers Biden to Warren, Warren to Sanders, and Sanders to Biden.
In technical terms, that's what we call
Notice, though, that even once Gillibrand, Hickenlooper, um... what'r'theirnames… uh.... I don't even remember who'all's dropped out because I can't remember who started anymore. Regardless, even with all of the people who have dropped out, there are still a whole lot of people nominally "in" the race who aren't going to get the nomination. And, even if it does come down to the probably top three candidates right now-- Biden, Warren and Sanders-- we are still dealing with the Arrow problem.
What does all of this mean? It's about the number of choices. More choices aren't intrinsically good. In psychology, you will encounter circumstances in which seeing too many choices can cause you difficulty. You get overwhelmed, and unable to make a rational choice individually because of the overload. Default to the familiar to escape the overload, and all of that. It's actually worse collectively because an election is not one decision. It is a group making a decision in which a plurality's choice (or some weird aggregation effect) is imposed even on those who didn't make it, which exacerbates everything.
What does that mean for winnowing? Well, it solves one problem. The paradox of choice. Get people like Gillibrand off the stage because she actually was causing a problem. A cognitive problem for voters. Every bit of time and space taken up by a sure-loser candidate adds cognitive difficulty to the task of choice between candidates with a chance at the nomination. That choice itself is beset by coordination problems between voters, which is hard enough anyway. It gets easier, though, with fewer distractions.
The actual "social choice" mechanics of choosing a candidate? That only works, according to the mathematics of Kenny, if you are looking at two choices, and nothing else. The problem-- ignored by damn-near everybody in my field who even knows about Arrow-- is that according to the man who was killed by bastards, if you are pretending that some option that actually could have been selected isn't really an option just to make your math work out, you cheated, and that cheat violates one of his rules.
Translation: If you start with anywhere north of two choices, and then winnow your field from 165,000,000 to two before holding your actual votes, you don't get to say, aha! We win, Kenny! Warren beat Biden, or Biden beat Warren, and it was democracy! We escaped your devious mathematics through the magic of winnowing! (And even this scenario doesn't work unless at least one of the following three drops out: Biden, Warren, Sanders. So, whose... "recording" do you want to be scarred for life by?)
Winnowing makes things nice and neat for the voters in practice, but it really isn't an escape. After all, if the candidates that you really liked wound up winnowed, your preferences-- your actual, underlying preferences don't get reflected in outcomes. If that's what democracy is all about, then this is all for show.
The greatest show on earth!