One commonly accepted axiom of choice theory is what's often called 'expansion consistency
', the idea of which is that if P is chosen from the set of P, Q, and R then adding S to the set shouldn't lead to P losing to either Q or R. (This is closely related to Arrow's Indepence condition
.) To give a trivial example, suppose that you have the option of vanilla or chocolate ice cream and choose vanilla. Then you're told that strawberry is also available. To say 'oh, well in that case I'll have chocolate' would seem odd, since chocolate was available before.
Note, however, that one isn't required to stick with one's original choice when the expanded set of options includes more attractive alternatives: it would be quite understandable for you to switch to strawberry ice cream if that is your favourite. This point seems lost of Stoke's Ryan Shawcross, who apparently decided to commit his footballing allegiance to England
before having the option of choosing Wales. Here's what he says:
"I made my decision a long time ago when the current rule wasn't in place that I could play for Wales.... My decision might have been different if the current rule was in place at the time but these things happen
A FIFA rule change in 2009 means that, though Shawcross wasn't previously eligible for Wales, he now is. But it seems that he's unwilling to consider switching allegiance, having decided to commit to England (when Wales wasn't an option). This is rather odd.
In effect, he's saying that he chose X when only X was available, and now that he has the choice of X or Y he's unwilling to consider Y, because of that prior decision. Of course, I'm not criticizing him for choosing England over Wales, but he admits that he might now have chosen differently. To regard himself as bound by a past decision, which was hardly really a choice, now that he has a wider range of options seems irrational.
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