I would chose red over blue. I would also chose blue and green over red and blue. However, my choices do not evidence a true preference. This is because of axiom 4, which is crucial. Axiom 4 actually defines what it means to prefer one bet over another. Preferences must be quantifiable, and I would not be able to quantify my preference. I could not say “I will take a boot to the head rather than cake if red is not chosen or three dice all roll 1s.” By the framework of axioms presented, I am actually indifferent among the bets presented.
This is actually an important distinction, as the objections to inconsistent ordering of values are based on someone making multiple choices/bets that make them better off that in aggregate make them worse off. No money pumps, no dutch books.
I would chose red over blue. I would also chose blue and green over red and blue. However, my choices do not evidence a true preference. This is because of axiom 4, which is crucial. Axiom 4 actually defines what it means to prefer one bet over another. Preferences must be quantifiable, and I would not be able to quantify my preference. I could not say “I will take a boot to the head rather than cake if red is not chosen or three dice all roll 1s.” By the framework of axioms presented, I am actually indifferent among the bets presented.
This is actually an important distinction, as the objections to inconsistent ordering of values are based on someone making multiple choices/bets that make them better off that in aggregate make them worse off. No money pumps, no dutch books.