![]() the best whatever actor 2 decides to do) so that considerations of rationality will compel him not to swerve. This means that his non-swerving strategy is now a dominant one (i.e. In the second game actor 1 has been able to place a side bet that obliges him to pay 2 units (to some third actor) if he chooses to swerve. (This' of course, would also be a mere accident, as Brouwer's theorem only states the existence of at least one fixed point.) Then the utility function u could be invoked in order to choose between these points, so that one should choose the x 1 giving the largest value u ( x 1) even if this would typically be a lower value than u (x). in the case where there are several fixed points x 1, x 2. Adopting a self-fulfilling belief for its causal efficacy would then require x = x, which could only arrive by accident. We then define x as the value of x that maximizes u = g (f (x)). Let us also assume that the conditions of Brouwer's fixed- point theorem are fulfilled, so that there exists an x such that x = f (x). Let us further assume that my utility u is a function g of y. More formally, let us assume that the state of the world y is a function f of my beliefs about the world x (and of a number of other factors that are kept constant for the purposes of this analysis). The point is that in some cases the belief may not only change the world in some (desired) manner but change it in a manner that makes the belief come out true. Section IX below for a brief discussion of this problem. also note 26 below, where the notion of public side bet is briefly defined.ġ2. If I can persuade myself to think that either I shall always resist the temptation to take a second helping of dessert or I shall never do so, then the chances are better that I shall never do so than if I make a separate choice at each occasion. ![]() It can then be shown that this method of decision delays the switch point and increases the proba bility that the larger reward will be chosen. Ainslie then imagines a case where a subject is offered a choice between two such rewards a number of times in succession: the private side bet is then a decision to choose between all pairs simultaneously instead of making a succession of choices. There is a switch point, that is, when the person stops preferring the large reward and begins preferring the smaller reward. (See Section V for the privi leged nature of exponential curves.) This means that the relative effectiveness of a large reward in the distant future and a smaller reward in the near future may change when the corresponding curves cross (which they can never do if they are exponential). We assume, furthermore, that the curve relating time to effectiveness is more concave than an exponential curve, e.g. We assume that present effectiveness of future reward is a decreasing function of the time from now till the reward is due. ![]() A brief explanation of this concept may be of interest. ![]() All subjects Allied Health Cardiology & Cardiovascular Medicine Dentistry Emergency Medicine & Critical Care Endocrinology & Metabolism Environmental Science General Medicine Geriatrics Infectious Diseases Medico-legal Neurology Nursing Nutrition Obstetrics & Gynecology Oncology Orthopaedics & Sports Medicine Otolaryngology Palliative Medicine & Chronic Care Pediatrics Pharmacology & Toxicology Psychiatry & Psychology Public Health Pulmonary & Respiratory Medicine Radiology Research Methods & Evaluation Rheumatology Surgery Tropical Medicine Veterinary Medicine Cell Biology Clinical Biochemistry Environmental Science Life Sciences Neuroscience Pharmacology & Toxicology Biomedical Engineering Engineering & Computing Environmental Engineering Materials Science Anthropology & Archaeology Communication & Media Studies Criminology & Criminal Justice Cultural Studies Economics & Development Education Environmental Studies Ethnic Studies Family Studies Gender Studies Geography Gerontology & Aging Group Studies History Information Science Interpersonal Violence Language & Linguistics Law Management & Organization Studies Marketing & Hospitality Music Peace Studies & Conflict Resolution Philosophy Politics & International Relations Psychoanalysis Psychology & Counseling Public Administration Regional Studies Religion Research Methods & Evaluation Science & Society Studies Social Work & Social Policy Sociology Special Education Urban Studies & Planning BROWSE JOURNALSĨ.
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