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Subject: Are Game Preferences Transitive? rss

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Bill Cook
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If you:

Prefer Game A over Game B, and
Prefer Game B over Game C

Do you necessarily prefer game A over C?


Side note for math geeks and/or dice fans:

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Thom0909
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So the big reveal in the video is not just the numbers on each die vary, but the frequencies do as well. Meh.

For game preferences, the transitive law applies (necessarily, I would say) if I assume all my paired preferences are stable and meaningful. They often aren't.



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Bryan Thunkd
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Re:
EMBison wrote:
Are Game Preferences Transitive?

If you:

Prefer Game A over Game B, and
Prefer Game B over Game C

Do you necessarily prefer game A over C?
I can't imagine a situation where, given games A, B & C, I wouldn't be able to pick a game that I'd prefer to play at that moment.

Prop Joe wrote:
if I assume all my paired preferences are stable
My preferences for games aren't necessarily fixed or stable. If I've played a lot of area control games recently, my preference for playing another area control game might be a lot lower than it would normally be, for example. And sometimes I might just "be in the mood" for one game more than another, while on another night the reverse may be true.

But at any given moment, I'd be able to rank three games in an order of my preference to play them in such a way that I either prefer one of the games or prefer all of them equally.
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Derry Salewski
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Do people actually view things that way?


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Larry L
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Prop Joe wrote:
So the big reveal in the video is not just the numbers on each die vary, but the frequencies do as well. Meh.



You can make non-transitive dice where all the numbers on a (each) single die are unique, but ties are avoided so within a set of dice, non-transitive dice do not share the same numbers.
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There can be exceptions, but I did a "quick-mapping" of some of the games I've encountered and find that for the most part, it works like that with me.
 
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P. Biensan
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In my experience preferences are not transitive, because the position of an item on your scale of enjoyment is not a single point, but a probability to find the item within a certain area of the scale. If three games A, B and C's areas are sufficiently far apart from each other, you can state confidently which one you like the most and which one you like the less. But if they're close, you cannot know which you like more until you actually make an "observation" (like, asking yourself, "if I had the choice between these two items right now, which would I chose?"), which makes the probability collapse to a single point, *but only for that particular observation*.

Thus, in that case, it is not only possible to like A more than B, B more than C, and C more than A, but it is also likely that you could get different results if you did the obversation again later.


Of course, since this only works for items which are close to each other on the scale, and since if you randomly pick a small number of items they are probalistically unlikely to be close on the scale, this becomes more apparent only if you do a systematic comparison of all the items.
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Laura Creighton
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When it comes to games I dislike, mostly yes. If I dislike a game it is usually about the game. When it comes to games I like, no, what game I prefer depends on whom I am considering playing it with. If that is not a constant, all bets on what I prefer go out the window. Even if those are held constant I often find that I prefer A over B, B over C and C over A. Often that means there is a serious downside to each choice .... but if we play that one I have to teach it, or I love this game but not with that person who pkays it badly/hates it/always wins. This generally means we should find something else to play.

Sometimes the conclusion to draw is that I really don't care what we play, they all are about the same to me. If they need a vote just roll a (fair) die.
 
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Boaty McBoatface
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EMBison wrote:
If you:

Prefer Game A over Game B, and
Prefer Game B over Game C

Do you necessarily prefer game A over C?


Side note for math geeks and/or dice fans:

For me yes, as my mind is not an equation.

To illustate.


I prefer Letter from whitechappel over Fury of Dracula (just).
I prerer Fury over Van Hesling (a bit more)
But Van Helsing is differnt enough from Letters for the two to not be quite comparable. THus I cannot say I prefer Letter over Van Helisng, only that which I mplay is based upon my mood.
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Bryan Thunkd
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slatersteven wrote:
For me yes, as my mind is not an equation.
I think you mean no actually. For something to be transitive then if A > B and B > C then it must be that A > C. If this doesn't apply then your preferences are not transitive.

slatersteven wrote:
I prefer Letter from whitechappel over Fury of Dracula (just).
I prerer Fury over Van Hesling (a bit more)
But Van Helsing is differnt enough from Letters for the two to not be quite comparable. THus I cannot say I prefer Letter over Van Helisng, only that which I mplay is based upon my mood.
But you are capable of choosing between them. If you truly had A > B, B > C, C > A preferences then you'd be stuck in an infinite loop. No matter which game you settled on, you'd always decide that you wanted to play another game more and start looping again.
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Bryan Thunkd
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PBiensan wrote:
In my experience preferences are not transitive, because the position of an item on your scale of enjoyment is not a single point, but a probability to find the item within a certain area of the scale. If three games A, B and C's areas are sufficiently far apart from each other, you can state confidently which one you like the most and which one you like the less. But if they're close, you cannot know which you like more until you actually make an "observation" (like, asking yourself, "if I had the choice between these two items right now, which would I chose?"), which makes the probability collapse to a single point, *but only for that particular observation*.
I don't see this as an invalidation of transitiveness. Preferences change over time. As a kid I didn't like Asparagus, now I do. But both then and now I could compare them to my preference for lima beans and transitively order my preferences.

Essentially your scenario is just an example of preferences changing over time, just very very quickly. At no given moment would you ever hold contradictory preferences (i.e. A > B, B > C, C > A). Every time you'd choose a game, or in your terminology... make an observation, your preferences would collapse into a transitive set. The fact that it might have gone differently a second prior or a second later is irrelevant. Your fickleness simply means that your preferences change often, not that they ever exist in a state where you'd have contradictory preferences.

Quote:
Thus, in that case, it is not only possible to like A more than B, B more than C, and C more than A, but it is also likely that you could get different results if you did the obversation again later.
Different results don't matter. My child self preferred broccoli to asparagus. My adult self prefers asparagus to broccoli. The fact that preferences change doesn't alter whether you can order those preferences in a transitive fashion or not. If you implanted a chip in my head that randomly flipped my preferences for asparagus and broccoli every nanosecond I'd still prefer one to the other at every given nanosecond despite the fact that those preferences are constantly changing.
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Dee Wongsa
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Context matters though. I might think that Game A > Game B when there are 4 players. And I think that Game B > Game C when there are 2 players. Do I prefer Game A over Game C? What if Game A doesn't have a 2 player variant and Game C only plays 2 players--then how could they be said to be comparable?
 
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mike hayes
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Transitivity of game preferences?

Lots of things in life are appreciated in a qualitative non-measurable fashion. Everything from a pleasant evening out to beautiful (wo)men to inspiring scenery. And yes, there are those people who enjoy converting such things into "marks" in restaurant guides, beauty pageants or tourist guides. And yes, there are BGG rankings that do this for games.

In my opinion, rankings and comparison are handy rules-of-thumb not to be taken too seriously. If you get obsessed with transitive rankings, that way, madness lies.
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Chris
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Yes and no. They're transitive on any given orthonormal basis vector but the preference phase space is higher dimensional and the selection criterion orthogonally varies with time.

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