"Independence of Irrelevant Alternatives"…..hmmmm

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    Hi Bob,

    I have finally made it through Part #1 of the History of Economic Thought and am now going through Part #2 and doing all of this via audio as I take my long drives….and it all worked “pretty” well until I got to this proof of the non-existence of a single function for assigning a societal selection/vote (Utility and Welfare).

    I don’t exactly have my finder on it, but I am having trouble with the second point around “Independence of Irrelevant Alternatives”, and before I step into the quicksand with a stupid comment, I need to watch the video version to see if any of your fancy mathematical notation handiwork make it all clear to me. (clear either way I suppose)

    Perhaps I am missing something in the assumptions….so let me at least ask that here. Do the people involved in this “voting” understand that their preferences are being pulled together by some hypothetical voting calculation to assign a social assignment (vote) for an outcome? (or are their preferences only private without any concern that others are involved in that calculation with their own preferences?)

    I feel my toe touching the quicksand, but let me go just a tiny bit further……if the people know about the existence of others in the calculation, I think I can see ways that a preference for “Vanilla over Chocolate” might change to “Chocolate over Vanilla when Strawberry” is added as a third option. (but for now, I will leave it there)



    There isn’t voting in the model per se. It is a logical framework, which supposes that people have genuine subjective rankings of all possible outcomes. It is a separate matter to figure out how, in reality, outsiders would extract that information.

    So I guess to be consistent with the “rational expectations” revolution (which we cover much later in the course), you would say that the people in Arrow’s model realize they are part of a society and that their individual preferences are being used as inputs for a broader judgment. But they are not allowed to lie about their preferences, if that’s what you’re getting at.


    Lie isn’t my point, but if they for example think that the choice is Chocolate and Vanilla, they might like them both very similarly, but enjoy chocolate just a tad more and so select it.

    But lets now say that the choice of Strawberry were thrown into the mix….what if it was generally known that when there are these three “candidates” in the running that the population preferences were very closely split between Strawberry and Vanilla with Chocolate being a distant third…..and if they did not like Strawberry nearly as much as either Chocolate or Vanilla (which between the two, they only slightly favored Chocolate)…..they might very well change their selection to vanilla knowing that doing so is more likely to get them some thing they desire vs something they do not.

    I know what you said…..they are not “voting”, but if they realize that are taking part in some sort of selection process, vote or not, they will operate in a manner that get them what is in their self-interest.

    I suppose I am mixing apples and oranges…..or maybe just polluting a theoretical over simplistic scenario with what I think are more typical real-world issues…..but I suppose this is my problem with economic theory as far as I understand it…..it seems to rely on static calculus….to me there seems to be a very large component effecting things from the “moving parts” and how fast and far they move. (working on speculation, fear, greed and the like)

    That is why I made a comment a while back about simulating things more like electronic circuits….for example, to me the economy is always adjusting…..so either it is always in equilibrium or it is NEVER actually in equilibrium…..I think the former, unless the change comes from some sort of genuine shock, and I don’t exactly know how to “quantify” that sort of stimulus.


    I (think I) get what you’re saying, but no, that kind of strategic consideration isn’t involved in Arrow’s Impossibility Theorem. It is assumed that the Social Welfare Ordering really operates on their people’s actual preferences.


    (Just to follow up: And so no, a person can’t “alter” his preferences in light of knowing that they are taken as inputs into a social choice.)

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