PREFERENCES

	Johnny von Neumann -- machine, game theory, dt, optimization -- math
	John Kemeny -- inventor of BASIC
	utility for one person
	 -----------
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	|   4.5
	|	44
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	strategic form payoff


	apples > oranges 
	an apple > an orange
	this apple > this orange   (=  apple813 > orange917 )

UTILITY THEORY

	u					rick
	u1
	u2
	utility functions
	domain:  quantity of commodities
	range:   real number; integer?

			real-valued utility 
			(long dutch tradition, jeremy bentham???)

	transformation:  nonlinearity

	u(an apple)
	u(apples)
	u(apple813)
	u(ronloui,apple813, Wed Sep 29 18:14:36 CDT 2004)
	u(ronloui,apple813, Wed Sep 29 18:14:36 CDT 2004,while you are dying in kosovo)

	mozart >(1) bartok
	bartok >(2) mendelssohn
	mendelssohn >(3) mozart

	mozart-bartok > bartok-mozart
	.
	.
	.

	menu-dependence

	u(apple813) = 43.5

	lottery:  u( { apple812)/.4; apple(813)/.6 } )
		= .4*u(applie812) + .6*u(applie813)

	totality of preference
	>= is a total order


	leonard savage -- 1951 found of statistics, 
		dt, 1970 phil of sci, problem of small worlds

	axioms of preference

	ordering is total, substitute a lottery for a certainty,
	you can substitute equivalents in a lottery

	guarantee that utility is unique up to affine transformation

	my scoring function is a multiattribute additive weighted
	utility

	u(a,b,c) = 5*a + 3*b - 1*c

	what if regularity isn't real?

	u(a,b,c) for all <a,b,c> in AXBXC

PROBABILITY

	1 raining dark 
	2 not-raining not-dark
	3 raining not-dark
	4 nor-raining dark

		Borel Set -- prob measure
		booleans on predicates/propositions -- Lindenbaum/Tarski algebra

					hw:  is there a notion of difference
					or multiplication in the temperature scale?

	p(1), p(2), p(3)...

	frame of discernment

	medical diagnosis symptoms --> ailments

	diagnosing failure in sony vaio pcg-505tr, p(S), |S| = ?

	prob(memory error | bus error) = prob (memory error & bus error) / prob (bus error)

	bayes rule

	loui's bad memory:

	p(good | sweet, red)  >= 1 - k - m 

	GIVEN:
	p(good | sweet) = 1 - k
	p(good | red) = 1 - m

	loui's bad memory:

	p(a | c) >= (1-k)(1-m)

	GIVEN:
	p(a | b) = 1-k ;  p(b | c) = 1-m


	independence p(a & b) = p(a) p(b)

	assume conditional independence:
	p(cancer | smoking)  = p(smoking | smoking, weak person)

	assuming this is like assuming preferences are transitive!

	IN OUR REASONING ABOUT THE WORLD:

		predictive

		informative

	causal screening