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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 11/20/2003 9:51 AM (GMT -6) |   | Hey, check THIS out: http://ratio.huji.ac.il/dp/Zamir343.pdf
I just read the first few pages. Looks like we're on to something with our 'indeterminacy logic', and we're not the first ones either.
Title and abstract:
Type Indeterminacy: A Model of the KT(Kahneman-Tversky)-man
Ariane Lambert Mogiliansky., Shmuel Zamir†and Hervé Zwirn
October 23, 2003
Abstract
In this note we propose to use the mathematical formalism of Quantum Mechanics to capture the idea that agents’ preferences, in addition to being typically uncertain, can also be indeterminate. They are determined (realized, and not merely revealed) only when the action takes place. An agent is described by a state which is a superposition of potential types (or preferences or behaviors). This superposed state is projected (or ”collapses”) onto one of the possible behaviors at the time of the interaction. In addition to the main goal of modelling uncertainty of preferences which is not due to lack of information, this formalism, seems to be adequate to describe widely observed phenomena like framing and instances of noncommutativity in patterns of behavior. We propose two experiments to test the
theory.
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DLW
Registered Member
Date Joined Apr 2003
Total Posts : 2457
| Posted 11/20/2003 10:08 AM (GMT -6) | | Kahneman and Tversky use experimental evidence to show how people tend to understand relatively small probabilities, inadequately. Either, they ignore the probabilities or when the probabilities are brought to their attention they assign more analytical weight to them than their probabilities would "objectively" warrant. This is why people buy lottery tickets, even when their expected return is well below what they spend on the ticket. They don't take into account the very low probability of winning adequately. It also helps insurance companies make more money since people are more willing to pay for insurance for insurance against relatively small probability events.
The implications of this is that often how a gamble is framed for individuals will affect whether they are willing to accept it or how much money they'd be willing to pay to take part in the gamble.
In standard economic theory, someone's willingness to pay is based on their expected utility, whereby the payoffs in different states of the world are aggregated linearly by their probabilities based on the deterministic utility associated with the outcome. K&T's theory shows that there are empirical regularities associated with our imperfect understanding of probabilities(to say nothing of situations of uncertainties when the probabilities associated with events are un-measurable due to the fact that the circumstances that govern them are not repeated indefinitely. This contrast social interactions with physical interactions. We may be able to predict the level of rainfall in a season for an area based on the past, but it is harder to assign a definite probability to someone reneging on a business contract and one's expected lawyer-expenses for a given period of time. )that contradict the prediction of the standard theory.
I haven't looked at the paper, but I will. However, it sounds like they are modifying the theory somewhat to account for these regularities.
Anyways, you all might want to crack open books on calculus-based probability if you're going to pursue this route further...
dlw
Niebuhr thought that sustained moral energy in politics depended on religion's power to mobilize reason along with self-transcending love. The prophetic tradition, meanwhile, gave Jews and Christians some protection against the temptation to identify their social causes with God's will. Lincoln's second inaugural address expressed the prophetic insight, "The almighty has His own purposes." | | Back to Top | | |
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