Personally, I think it clarifies things—though at the expense of introducing complication. People disagree over which bet the problem represents. Describing those bets highlights this area of difference.
I see what you mean. But some comments have said, “I can set up a payoff scheme that gives this answer; therefore, this is an equally-valid answer.” The correct response is to state the payoff scheme that gives your answer, and then admit your answer is not addressing the problem if you can’t find justification for that payoff scheme in the problem statement.
It is both bad and confusing that people are defending the idea that this problem is not clearly-stated enough to answer.
I suspect this happens because, people don’t like criticising the views of others. They would rather just say ‘you are both right’ - since then no egos get bruised, and a costly fight is avoided. So, nonsense goes uncriticised, and the innocent come to believe it—because nobody has the guts to knock it down.
Re: “Introducing a payoff only confuses matters.”
Personally, I think it clarifies things—though at the expense of introducing complication. People disagree over which bet the problem represents. Describing those bets highlights this area of difference.
I see what you mean. But some comments have said, “I can set up a payoff scheme that gives this answer; therefore, this is an equally-valid answer.” The correct response is to state the payoff scheme that gives your answer, and then admit your answer is not addressing the problem if you can’t find justification for that payoff scheme in the problem statement.
Indeed—that would be bad—and confusing.
It is both bad and confusing that people are defending the idea that this problem is not clearly-stated enough to answer.
I suspect this happens because, people don’t like criticising the views of others. They would rather just say ‘you are both right’ - since then no egos get bruised, and a costly fight is avoided. So, nonsense goes uncriticised, and the innocent come to believe it—because nobody has the guts to knock it down.