Transitivity of preferences

Economics Economics Questions
1

Hey,

I have read somewhere that praxeology does not assume the transitivity of preferences, which is one of the most basic assumptions of neoclassical consumer theory. The assumption of transitivity states that if a consumer prefers A to B and B to C, then said consumer would prefer A to C. Does praxeology avoid this assumption because of a problem with cardinality and utility calculations? I would have thought that it is perfectly compatible with the ordinal nature of utility.

Any thoughts please.

2

IIRC, according to Jeff Heberner’s Mises U lecture on utility, to Austrians, preference IS transitive, at least at any given time. Of course, across time, value scales change, so transitivity isn’t applicable intertemporally.

3

Fred:

The attempt has been made to attain the notion of a nonrational action by this reasoning: If a is preferred to b and b to c, logically a should be preferred to c. But if actually c is preferred to a, we are faced with a mode of acting to which we cannot ascribe consistency and rationality. This reasoning disregards the fact that two acts of an individual can never be synchronous. If in one action a is preferred to b and in another action b to c, it is, however short the interval between the two actions may be, not permissible to construct a uniform scale of value in which a precedes b and b precedes c. Nor is it permissible to consider a later third action as coincident with the two previous actions. All that the example proves is that value judgments are not immutable and that therefore a scale of value, which is abstracted from various, necessarily nonsynchronous actions of an individual, may be self-contradictory.[7]

One must not confuse the logical concept of consistency (viz., absence of contradiction) and the praxeological concept of consistency (viz., constancy or clinging to the same principles). Logical consistency has its place only in thinking, constancy has its place only in acting.

Constancy and rationality are entirely different notions. If one’s valuations have changed, unremitting faithfulness to the once espoused principles of action merely for the sake of constancy would not be rational but simply stubborn. Only in one respect can acting be constant: in preferring the more valuable to the less valuable. If the valuations change, acting must change also. Faithfulness, under changed conditions, to an old plan would be nonsensical. A logical system must be consistent and free of contradictions because it implies the coexistence of all its parts and theorems. In acting, which is necessarily in the temporal order, there cannot be any question of such consistency. Acting must be suited to purpose, and purposefulness requires adjustment to changing conditions.

(Human Action, Section: The Temporal Relation Between Actions)

4

Thanks Adam and Lilburne.

So the idea is that if one were to take any instance in time, preferences would indeed be transitive. However, this property cannot be applied inter-temporarily. So the error lies in treating preferences and actions (which act upon these preferences) as both having the transitive characteristic?

On the other hand, take this as an example:

at time t0) A is preferred to B, and B is preferred to C.

at time t1) C is preferred to B, and B is preferred to A.

At both instances in time, preferences have the characteristic of being transitive. Of course, the preferences themselves have changed, and thus so has the transitivity, but transitivity changes merely to reflect changes in preferences themselves. It does not break down as such.

5

Hi Fred.

Your example:

"On the other hand, take this as an example:

at time t0) [A is preferred to B] and [B is preferred to C]."

I think what Mises is trying to say, and what you may be missing, is that in his conception of preference, there are only 2 “categories” so to speak: that which is chosen (preferred), and that which is set aside.

Your example shows two instances of preferring by Mises’s conception (i.e., two sets of two categories). So by Mises’s conception, those are two separate acts.

I’m not sure whether you’re seeing Mises’s meaning.

I think you can see it more clearly if you extend the series you are using as an example:

at time t0) A is preferred to B, and B is preferred to C, and C is preferred to D, and D is preferred to E, and E is preferred to F, and F is preferred to G, and G is preferred to H…

Then, is this a formal-logical construct, or a description of action in the temporal order?

Mises is saying that if it is a formal construct, it is “a-temporal.” If it is a description of action, each listed preference is a separate act of preference:

act 1: preferring A to B

act 2: preferring B to C

act 3: preferring C to D

etc…

I think if you read Mises’s passage with this in mind, you may better catch his meaning.

6

Another way to see it:

When the word preference is used, substitute the term “act 1” for the first time it is used, insert “act 2” for the second time it is used, etc…

I.e., each reference to the concept “preference” will refer to a separate act in the temporal order…

7

Transitivity holds for neo-classical models because they’re dealing with compressed logical time. There are no intervals and human action is ignored. If you compress time into an instantaneous decision, then A>B>C=A>C.

8

Well said !