Certainly an objective outside observer who is somehow allowed to ask the question, “Has somebody received a green ball?” and receives the answer “yes” has learned nothing, since that was guaranteed to be the case from the beginning. And if this outside observer were somehow allowed to override the participants’ decisions, and wished to act in their interest, this outside observer would enforce that they do not take the bet.
But the problem setup does not include such an outside objective observer with power to override the participants’ decisions. The actual decisions are all made by individual participants. So where do the differing perspectives come from?
Perhaps of relevance (or perhaps not): If an objective outside observer is allowed to ask the question, “Has somebody with blonde hair, six-foot-two-inches tall, with a mole on the left cheek, barefoot, wearing a red shirt and blue jeans, with a ring on their left hand, and a bruise on their right thumb received a green ball?”, which description they know fits exactly one participant, and receives the answer “yes”, the correct action for this outside observer, if they wish to act in the interests of the participants, is to enforce that the bet is taken.
I am trying to point out the difference between the following two:
(a) A strategy that prescribes all participants’ actions, with the goal of maximizing the overall combined payoff, in the current post I called it the coordination strategy. In contrast to:
(b) A strategy that that applies to the single participant’s action (me), with the goal of maximizing my personal payoff, in the current post I called it the personal strategy.
I argue that they are not the same things, the former should be derived with an impartial observer’s perspective, while the later is based on my first-person perspective. The probabilities are different due to self-specification (indexicals such as “I”) not objectively meaningful, giving 0.5 and 0.9 respectively. Consequently the corresponding strategies are not the same. The paradox equate the two,:for pre-game plan it used (a), while for during-the-game decision it used (b) but attempted to confound it with (a) by using an acausal analysis to let my decision prescribing everyone’s actions, also capitalizing on the ostensibly convincing intuition of “the best strategy for me is also the best strategy for the whole group since my payoff is 1⁄20 of the overall payoff.”
Admittedly there is no actual external observer forcing the participants to make the move, however, by committing to coordination the participants are effectively committed to that move. This would be quite obvious if we modified the question a bit: If instead of dividing the payoff equally among the 20 participants, say the overall payoff is only divided among the red ball holders. (We can incentivize coordination by letting the same group of participants play the game repeatedly for a large number of games.) What would the pre-game plan be? It would be the same as the original setup: everyone say no to the bet. (In fact if played repeatedly this setup would pay the same as the original setup for any participant). After drawing a green ball however, it would be pretty obvious my decision does not affect my payoff at all. So saying yes or no doesn’t matter. But if I am committed to coordination, I ought to keep saying no. In this setup it is also quite obvious the pre-game strategy is not derived by letting green-ball holders maximizing their personal payoff. So the distinction between (a) and (b) is more intuitive.
If we recognize the difference between the two, then (b) does not exactly coincide with (a) is not really a disappointment or a problem requiring any explanation. Non-coordination optimal strategies for each individual doesn’t have to be optimal in terms of overall payoff (as coordination strategy would).
Also I can see that the question of “Has somebody with blonde hair, six-foot-two-inches tall, with a mole on the left cheek, barefoot, wearing a red shirt and blue jeans, with a ring on their left hand, and a bruise on their right thumb received a green ball?” comes from your long held position of FNC. I am obliged to be forthcoming and say that I don’t agree with it. But of course, I am not naive enough to believe either of us would change our minds in this regard.
I’m not sure what you’re saying here.
Certainly an objective outside observer who is somehow allowed to ask the question, “Has somebody received a green ball?” and receives the answer “yes” has learned nothing, since that was guaranteed to be the case from the beginning. And if this outside observer were somehow allowed to override the participants’ decisions, and wished to act in their interest, this outside observer would enforce that they do not take the bet.
But the problem setup does not include such an outside objective observer with power to override the participants’ decisions. The actual decisions are all made by individual participants. So where do the differing perspectives come from?
Perhaps of relevance (or perhaps not): If an objective outside observer is allowed to ask the question, “Has somebody with blonde hair, six-foot-two-inches tall, with a mole on the left cheek, barefoot, wearing a red shirt and blue jeans, with a ring on their left hand, and a bruise on their right thumb received a green ball?”, which description they know fits exactly one participant, and receives the answer “yes”, the correct action for this outside observer, if they wish to act in the interests of the participants, is to enforce that the bet is taken.
I am trying to point out the difference between the following two:
(a) A strategy that prescribes all participants’ actions, with the goal of maximizing the overall combined payoff, in the current post I called it the coordination strategy. In contrast to:
(b) A strategy that that applies to the single participant’s action (me), with the goal of maximizing my personal payoff, in the current post I called it the personal strategy.
I argue that they are not the same things, the former should be derived with an impartial observer’s perspective, while the later is based on my first-person perspective. The probabilities are different due to self-specification (indexicals such as “I”) not objectively meaningful, giving 0.5 and 0.9 respectively. Consequently the corresponding strategies are not the same. The paradox equate the two,:for pre-game plan it used (a), while for during-the-game decision it used (b) but attempted to confound it with (a) by using an acausal analysis to let my decision prescribing everyone’s actions, also capitalizing on the ostensibly convincing intuition of “the best strategy for me is also the best strategy for the whole group since my payoff is 1⁄20 of the overall payoff.”
Admittedly there is no actual external observer forcing the participants to make the move, however, by committing to coordination the participants are effectively committed to that move. This would be quite obvious if we modified the question a bit: If instead of dividing the payoff equally among the 20 participants, say the overall payoff is only divided among the red ball holders. (We can incentivize coordination by letting the same group of participants play the game repeatedly for a large number of games.) What would the pre-game plan be? It would be the same as the original setup: everyone say no to the bet. (In fact if played repeatedly this setup would pay the same as the original setup for any participant). After drawing a green ball however, it would be pretty obvious my decision does not affect my payoff at all. So saying yes or no doesn’t matter. But if I am committed to coordination, I ought to keep saying no. In this setup it is also quite obvious the pre-game strategy is not derived by letting green-ball holders maximizing their personal payoff. So the distinction between (a) and (b) is more intuitive.
If we recognize the difference between the two, then (b) does not exactly coincide with (a) is not really a disappointment or a problem requiring any explanation. Non-coordination optimal strategies for each individual doesn’t have to be optimal in terms of overall payoff (as coordination strategy would).
Also I can see that the question of “Has somebody with blonde hair, six-foot-two-inches tall, with a mole on the left cheek, barefoot, wearing a red shirt and blue jeans, with a ring on their left hand, and a bruise on their right thumb received a green ball?” comes from your long held position of FNC. I am obliged to be forthcoming and say that I don’t agree with it. But of course, I am not naive enough to believe either of us would change our minds in this regard.