# Critically Assess Broome’s Use of Finer Individuation to Defend Transitivity

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Critically assess Broome’s use of finer individuation to defend transitivity

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Expected Utility Theory (EUT) is one of the fundamental theory in Decision Theory. For EUT to be tenable, axioms has been proposed. Transitivity is one of them, which suggested that when there are choices, say a,b and c, if a>b and b>c, then a > c. This axioms has long been accredited.Yet, an counter example was provided, where when a>b, b>c and c>a, transitivity will no longer hold. Broome responded by saying that the “a” is “when a and b are compared” in a>b and the “a” is “when a and c are compared” in c>a, and thus in these cases are different and transitivity was no violated. This is known as fine individuation.

On the first sight, it may seems whenever transitivity is violated, fine individuation can be applied and every counterexample can no longer be valid. However, if we could add the criteria where the individuation could apply and limit the usage of fine individuation.

At the minimal level, we can add a rational principles of indifference. We need to first assume that people are ration, which decision theory always does. Then, we add that the “A when B” and “A when C” are indifferent. For example, if A is go to hike, B is staying at home and C is shopping, it is possible that if I go to hike because staying home is too boring in A > B and I stay at home because I have had many clothing already in C>A.  Too boring and having many clothing can be indifference as by nature, they are not comparable at all. The idea of rational principle of indifferent has it application in ethics. Broome (1991) mentioned that Jeremy Bentham believed pleasure is the only good and pain is the only bad, and when options gave same pleasure and same pain, it is irrational to have preference between these alternatives.

Broome (1991) explained in the sense of practical and non-practical preference. “A when B” and “A when C”, according to Broome are 2 choice that could happened at the same time in the real world and thus he called it non-practical. These kind of non-practical preference should not be taken into account into transitivity as this would be irrational and violate the fundamental assumption of decision theory – rationality. If people insist comparing the 2 non-practical choices, rational principles of indifference, as discussed above, should be introduced to keep the requirement of transitivity from being empty Moreover, Broome (1991) also if we followed the extreme Humean way, practical preference should not be constrained by transitivity. Surely, at least for me, this ideal would not attract me much as now we are discussing how we could avoid transitivity being empty and if we open transitivity as not being a requirement, this would not be appealing. But here I pointed out this idea for whom are extreme Humean only.

It should be noted that whenever fine individuate applies, the individuated option should be justifiable. For examples, we cannot say we prefer hiking to staying at home because I love shopping. It is totally irrelevant, or some vague reasons like I love meeting with friends so I go hiking, which staying home could meet friends too.

Pettit's analyses the fine individuation by prospect and property. Individuation by Properties counter two options as different if there is some properties in that options makes a difference in people’s preference, and individuation count two options as different just by whether one will prefer one another. Say, if I prefer hiking because of boring staying at home versus I prefer hiking because of hiking brings happiness that staying at home count, and thus prefer hiking to staying at home. If it is analyzing by the concept of individuation by properties, these two makes different because the reasons of staying at home is different, while by individuation of prospect, because both yield the preference of “hiking > staying at home”, they count the same options. Therefore, if we are using individuation by properties, when A>B, B>C, C>A, whether it is transitive would be the preference of “A in A vs B” and “A in A vs C”. If we are to say it is individuation by properties, they are not comparable as they are different options. Thus defining what individuation would be important.

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