Page 42-44, Non Linear Preference, “The money-pump concept also reveals a narrow perspective on how choice might be based on preferences, and perhaps a lack of imagination in dealing with cyclic patterns. Although there is no transparent way to make a sensible choice from {p,q,r} when p>q>r>p, nothing prevents a person from considering preferences over the set of convex combinations of p, q, and r. And, if there is a combination in the set, then that persons has an ex ante maximally preferred alternative. As first shown in Kreweras (1961), this indeed can be the case, and we shall consider it later as part of the SSB theory.”
Indeed; but I can still money pump you for cyclic preferences if I’m the only trader around, and I only offer you the pure lotteries p, q and r rather than convex combinations. And if you never change your preferences after you realise what I’m doing...
Restrictive conditions, to be sure, but mathematically you can’t escape. The fact that you generally do escape implies that something else is going on than your simple preferences.
Page 42-44, Non Linear Preference, “The money-pump concept also reveals a narrow perspective on how choice might be based on preferences, and perhaps a lack of imagination in dealing with cyclic patterns. Although there is no transparent way to make a sensible choice from {p,q,r} when p>q>r>p, nothing prevents a person from considering preferences over the set of convex combinations of p, q, and r. And, if there is a combination in the set, then that persons has an ex ante maximally preferred alternative. As first shown in Kreweras (1961), this indeed can be the case, and we shall consider it later as part of the SSB theory.”
Here is a modern paper addressing some of these issues: http://hal.archives-ouvertes.fr/docs/00/08/43/90/PDF/B06008.pdf
Indeed; but I can still money pump you for cyclic preferences if I’m the only trader around, and I only offer you the pure lotteries p, q and r rather than convex combinations. And if you never change your preferences after you realise what I’m doing...
Restrictive conditions, to be sure, but mathematically you can’t escape. The fact that you generally do escape implies that something else is going on than your simple preferences.