Right: you mean that every position will be either +-, = or -+. As for the "perfect move", there are obvious "clarifications" for winning or lost positions: i.e., for a "won game", the move(s) that result in checkmate in the least number or moves; for lost positions, the move(s) that result in checkmate in the most number of moves. The difficulty is in the "clarification" of equal positions; even if the initial position is =, almost everyone grants that White has some practical advantage, so it may make some sense to define the "perfect move" that maximizes (minimizes) the length of the game when White (Black); this type of "clarification" is not without flaws: e.g., consider two essentially equivalent positions except that the colours are reversed.

No, he means every position will be either 1-0, 1/2-1/2, or 0-1. That's what he said.

By the way, why is a shorter win more perfect than a longer win? Does prettiness count for anything? Is it more perfect if it contains less branches for you to go wrong? Why do you get to decide the definition of perfect instead of the people who developed the whole concept of game theory and solved games?

That's what he "said" (posted), but likely not exactly what he meant.

Well, I didn't decide this; in the context of chess, considering chess composition, often stipulations are "White to play and win" or "Mate in X"; therefore, minimal path to checkmate is an obvious "clarification" for decisive positions. It's for "equal" positions where there is ambiguity; e.g., if chess is a theoretical draw, it's very likely that many moves retain equality. Aesthetics won't necessarily play any role whatsoever: e.g., one can simply use criteria based on game length and number of possible future positions that retain equality. Besides, if one uses the definition simply based on game theory without considering the context of the history of the game of chess, one is missing the point, especially when considering that chess composition is arguably a form of art: e.g., in many chess problems such as "Mate in X", every legal possibility keeps the position "winning". I suppose if FIDE did not award IM or GM titles for the discipline of study or problem composition and "solving", then one may have an argument in using the game theoretic definition without any "clarification" whatsoever (despite the obvious ambiguity).

Game theory applies just fine to solving. Instead of playing the game out, the game is decided at (or before, if you stalemate/insufficient material) the desired number of moves. If white mates on or before that move, he wins. If he doesn't, he loses. Only solutions, and not moves that would win if this were normal chess, keep the game in the 1-0 evaluation.

Sure, that applies to problems only, but not to studies.

There are two different ways to go about which seem to get mixed sometimes.

1) We just look at the position. It is either won, drawn or lost for white. Each move that changes the evaluation of the position is a mistake. There is no place for aesthethics, it doesn't matter how long a game lasts, how difficult a position is to play etc.

2) We take it as a fact that chess players are human and can err. Then there are more than only three possible evaluations. For example, it's better to have R+B vs R than vice versa in a drawn endgame. We can make fine distinctions in the evaluation of positions and moves.

Before we argue about perfect games we have to define a perfect move. According to 1) each move that doesn't change the evaluation of the position is perfect. From this point of view there probably are tens of thousands of "perfect" games.

Factoring in humans inability a definition of a perfect move involves some subjective measures. One definition of the best move could be: The move that promises the most points against this opponent. Another one for won and lost positions: The move that forces the mate in the smallest number of moves/delays the mate the longest. There are a number of possible definitions and it depends on the definition if a game could be perfect or not.

I think that that's exactly what he meant, and I find it annoying that you are being so (willfully?) dense.

Sure, but any winning (or drawing) move in a study is equally valid and obeys normal chess rules. If there's some random 20 move win in addition to a cute fast win, both are equally valid- it's the study that sucks. You don't have to change the rules for "Win as white", just for "mate in X or fewer".

Pretty sure you're wrong.

You can come up with a bunch of interesting metrics that approximate the human concept of a good move and can distinguish between two moves that both lead to the same result assuming perfect play afterwards.

A simplistic example would be to say that move A is better than move B if a random game played from the resulting position has a higher expectation.
I'm sure people could come up with more interesting examples if they wanted to.

This is not just a practical issue, thinking in these terms could reveal information about the internal structure of games. E.g. can chess be played perfectly by applying a small set of simple rules and limited move by move analysis or do you need to calculate a lot of moves ahead to be sure you're playing a GT perfect move? I realize I didn't define rules and calculating moves in a mathematical sense but I think it's clear it could be done.

These are all good points. Once all the possible moves from a given position are classified as either "win in x", "loss in x", or "draw"... If you're playing against an opponent who knows the optimal strategy, there's nothing more to determine. But otherwise, it could make sense to apply further analysis to the losses and the draws. For the losses, you don't necessarily take the one that allows you to last the longest. You could select a losing move that loses quicker against optimal play, if you think there's a higher probability your opponent will make a mistake from that position. Similarly you can apply some heuristic to the drawn positions to determine win probability (only against a suboptimal opponent).

As a refinement to the random move heuristic, you could simulate the opponent's response using a fast but suboptimal chess engine (adding in a stochastic component to the evaluation function), and select whatever move gave the best results over 100 simulated games or however many there was time to simulate. I wonder if any chess engines with tablebases do this from solved positions? Wouldn't matter against another chess engine that had access to the same tablebase, but against human opponents it would.

I very strongly doubt there's a simple set of rules for evaluating chess position as win, loss, or draw without lookahead. But if you wanted to pursue that line of thinking, I'd suggest starting off with much simpler games that are already solved. Even something as simple as Tic Tac Toe. We already know which positions are won, lost, or drawn. Can you describe a SIMPLE set of rules without lookahead that perfectly classifies all possible Tic Tac Toe positions? Then if you can do that, work your way up to more complex, but still solved, games. How about Connect Four? Basically if you can't do this for simpler games, forget about classifying chess positions in this way.