Posts Tagged ‘preference’

Ideas of Choice

Monday, 11 November 2019

I have been more actively working on the decision-theory paper off of which the probability paper was spun. And this effort has me thinking about the meanings of choice.

As I noted in an earlier entry to this 'blog, my paper on indecision used choice to mean no more or less than selection. I defined relations of preference in terms of choice functions, which are functions that select a subset from a set of options. Defining relations of preference in this manner seems to explain preference in terms of something called choice rather than explaining the thing called choice in terms of preference. But something called choice is often said to result from preference. Certainly, we want somehow to explain selection by persons of alternatives (even if that which explains cannot itself be observed directly!), and some notion of preference represents an attempt at explanation.

(However, if preference is the proper explanation, then preference must be very changeable; much of real-world behavior does not conform to a constant set of preferences. And people do such things as regularly selecting {A} from a set {A, B, C} yet consistently selecting {B} from a set {A, B, D}; perhaps in such cases we can still contrive an explanation in terms of preference, but we should be dubious of such explanation. I don't think that we should reject the word choice if the selections that people actually make aren't driven by preference. If preference does not provide a proper explanation, then perhaps some more general concept does. And perhaps by teasing-out what people intend by the word choice when they intend something narrower than selection, we can arrive at that generalization. That's one of the reasons that I sometimes press some people, especially fellow economists, to tell me what they intend by the word choice or by coördinate terms, when they reject its application where it seems to me to fit. I'm not trying to catch them in error or Socratically to teach a lesson to them; I'm trying to engage with them in an important investigation. But, important doubts about the use of preference in descriptive theory not withstanding, preference makes considerable sense in prescriptive use. Indeed, that sense in prescriptive use is one of the reasons that we so easily accept it in descriptive use, and even assures us that it must at least approximate a realistic description fairly well, because unreasonable behavior is costly.)

Identification of a preference is sometimes itself called choice; but sometimes preference is instead expressed in terms of whom or of what one would choose, if given the choice; and, sometimes, after a preference is expressed, the response is something such as You don't get to make that choice! In conscious identification of a preference, one selects an ideation; in reporting such an identification, one selects an utterance; and these ideations or utterances are selected in a different way than are their subjects, except in odd, self-referential cases.

In discussion of decision-making in a world of uncertainty, I've found use for an idea that I call practical choice, by which I mean selection of an option which selection causes that option to be effected with certainty.

In a world without uncertainty, there would be a simple division between what one could attain and what one could not. Preference amongst the unattainable would ex definitione be without practical significance. Discussion of preference amongst the possible would be operationally equivalent to discussion of practical choice, and rational agents would always attain that possible state-of-the-world that they most desired.

When we begin to speak and write of uncertainty, we are actually speaking and writing of cases in which we may make practical choices amongst options that would, in turn, affect the state-of-the-world in imperfectly predictable ways. Hypothetically, I might not care about those effects; I might only care about the options that I can practically choose; but, with those options properly identified, that hypothetical is highly implausible and sterile. And, otherwise, it now becomes quite relevant to consider the difference and relationship between preferences amongst things that are subject to practical choice and preferences amongst things that are not subject to practical choice. Preferences amongst things that an agent cannot practically choose will determine preferences amongst things that she can.

(Our practical choices are more limited than some might at first realize. An agent has practical choice of no more than some mental states; and selecting amongst these mental states delivers no more power over other possibilities than to increase or decrease the probabilities of those possibilities. Given the selection of one mental state, one's arm is more likely to move, but there is at least some terrible possibility that it will not. Indeed, given the selection of one mental state, one is more likely to recall a desired datum, but there is a possibility that one will not. Still, in many cases we might, without doing too much violence to realism, pretend that our practical choices include operations that we think almost surely to follow upon our exercise of actual practical choice. For example, one might calculate as if one had a practical choice of whether to propose marriage, while acknowledging that one did not have a practical choice over whether one would marry the other party.)

The concern of my paper on indecision was in identifying a difference in observable behavior distinguishing indecision from indifference, and I didn't want that distinction to be simply self-reported. When an agent was undecided between X and Y rather than indifferent, I needed a difference in selection from a set in which X and Y options, rather than a difference in selection amongst utterances or somesuch. In hindsight, I wish that, in that paper, I'd discussed conceptions of choice more than I did, and had explicitly written of practical choice. Perhaps accordingly I will someday revise the working version of the paper.

Symbols for Preference Relations

Tuesday, 5 April 2011

Since some of the recent visits to this 'blog are by way of search strings containing preference symbol, I put together a table of characters frequently used to represent preference relations. Click on the graphic [detail of screen-shot of PDF file] for a PDF file providing symbols, their interpretation, their Unicode values in hexadecimal and in decimal, the names given to these symbols by the Unicode Consortium, and the LAΤΕΧ mark-up that one would enter for each of the symbols.