A number of assumptions are typically made on preferences to give so-called "well-behaved indifference curves"

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The consumer choice theory aims, among other things, at modeling preferences that will guide the consumer in his choices. To do this, an assumption will be made: the consumer is able to rank any two consumption bundles as to their desirability, that is, the consumer is aware of his own tastes and knows how to use them rationally in order to maximize his utility. In the neoclassical model, preferences relations are established following from an evaluation of the consumer's behaviour. Hence, it is considered that if he always chooses a consumption bundle A over a consumption bundle B, even where B is available and affordable, then A is strictly preferred to B (A > B). Similarly, other preferences relations are recognised: indifference (A ~ B) which means that A is equally preferred to B and vice versa; weak preference (A ≥ B) which means that A is preferred at least as much as B. An indifference curve (IC) is a set of bundles all equally preferred to each others. In other words, the IC that goes through A is the set of all bundles y such that A ~ y.

Extraits

[...] In the former case, the consumer acts as a fully informed individual, and his choices and preferences are modelled with standard neo- classical ICs. What is important in the choice-making process is how much the consumer feels informed, rather than how much he really is. In the latter case, the consumer is in a situation of uncertainty. If he uses the mobile phone, he is gambling on how bad it is for his health. However, preferences as well as ICs can still be drawn assuming perfect knowledge: the consumer is expected to be able to choose a combination of the three goods (mobiles, landlines, and health). [...]

[...] The last two assumptions will allow us to know the shape of a well-behaved IC. Continuity The sets : A and : A are closed sets, i.e. they contain their own boundaries. Such a technical assumption is required rule out some kinds of complicated discontinuous/jumpy behaviour”[1]. It implies that for a given set of preferences, a utility function is to be obtained so that if A then U(B). Monotonicity This assumption relies on the idea that the more is always preferred to the less. [...]

[...] Of all the assumptions made on preferences to give so-called behaved preferences”, we have seen that none of them appears to be absolutely unreasonable, and even that most of them not only hold, but are also essential for a best choice to exist. It is not difficult to isolate some cases where they do not hold, but that should not be seen as a failure of the model, for it primarily aims at describing general features of the choice-making process of consumers according to their preferences, not at catching all possible situations. [...]

[...] Indeed, transitivity implies that if A > B and B > then A > C. If it was not for transitivity, we could imagine a situation where A > B > C and C > A. But then, it would be impossible for the consumer to maximize his utility as there would always be a better choice than any he would make. This means that ICs cannot cross. Assumptions specific to well-behaved indifference curves Well-behaved indifference curves are assumed to be continuous, monotonic and convex. [...]

[...] Varian, Intermediate Microeconomics : A modern Approach, 6th edition, Norton The more the better The less the better û Á @ B Ò Ô ºÂæζž‰{jYjHjHjHjHjH7 hŠi®h'=\OJ[6]QJ[7]^J[8]mH sH ¹OJ[9]QJ[10]^J[11]mH sH hŠi®h+XOJ[12]QJ[13]^J[14]mH sH hŠi®h(JsOJ[15]QJ[16]^J[17]mH sH hŠi®OJ[18]QJ[19]^J[20]mH sH (hŠi®hŠi®CJ$OJ[21]QJ[22]^J[23]aJ$mH sH .hŠi®h(Js5?CJ0OJ[24]QJ[25]\?^J[26]aJ0mH sH .hŠi®hŠi®5?CJ0OJ[27]QJ[28]\?^J[29]aJ0mH sH .hŠi®hNegative slope of ICs resulting from monotonicity Moving on higher downward-sloping ICs (i.e. moving toward the preferred set) implies getting more of x and y whereas in the case of upward-sloping ICs, it requires to forgo some of x and/or some of y. So if the more is preferred to the less, the IC must be downward-sloping. [...]