Fair Bets Research Articles

A comment on Paul, Weinbach, and Wilson’s (2004) “Efficient markets, fair bets, and profitability in NBA totals 1995-96 to 2001-02”

This paper revisits Paul et al. (2004) using a more recent data set to test for inefficiencies in the totals market for NBA games. Using data from the 1995-96 to 2001-02 seasons, Paul et al. (2004) found the market as a whole to be efficient, but that this was not the case for bets on the highest of point totals. Using data from the 2012-13 to 2018-19 seasons reveals a market that is more efficient than that of their earlier work, as the null hypothesis of a fair bet is not rejected for the higher totals. However, winning percentages in excess of 52.4 % were found further in the upper tail of the distribution of points totals relative to the earlier period.

Household Wealth and Portfolio Choice When Tail Events Are Salient

Robust experimental evidence of systematic violations of expected utility (EU) establishes that individuals facing risk overweight utility from low probability gains and losses when making choices. These ndings motivated development of models of preferences with probability weighting functions, such as rank dependent utility (RDU). We solve for the optimal investing strategy of an RDU investor in a dynamic binomial setting from which we derive implications for investing behavior. We show that relative to EU investors with constant relative risk aversion, commonly measured probability weighting functions produce optimal RDU terminal wealth with signicant downside protection and upside exposure. We additionally nd that in contrast to EU investors, RDU investors optimally choose a portfolio that contains fair bets that provide payos that can be interpreted as lottery outcomes or exposure to idiosyncratic returns. In a calibrated version of the model, we calculate that RDU investors would be willing to pay 5% of their initial wealth for the freedom to trade away from an optimal EU wealth allocation. The dynamic trading strategy that supports the optimal wealth allocation implies portfolio weights that are independent of initial wealth but requires higher risky share after good stock return histories. Optimal trading also implies the possibility of non-participation when historical returns are poor. Our model lls a gap in the literature by providing new quantitative and qualitative predictions that can be tested experimentally or using data on household wealth and portfolio choice.

Introduction to the Special Issue Epistemic Aspects of Many-Valued Logics

The papers in this special issue are based on presentations delivered at the conference Epistemic Aspects of Many-valued Logics, held at the Institute of Philosophy of the Academy of Sciences of the Czech Republic, in Prague, 2010. All papers consequently revolve around the application of non-classical logical tools— mathematical fuzzy logic and/or probability theory—to epistemological issues. Timothy Williamson employs a modal epistemic logic enriched with probabilities to generalize an argument against the KK-principle. He argues that we can know a proposition even if our evidential probability for that proposition is low. In fact he argues that the evidential probability of a known proposition can be (arbitrarily) close to 0. The argument is first presented with a basic idealized model, which is then extended to much more complicated and realistic models. This then raises a problem for decision theory, since you can know that p, while your evidence tells you (strongly) that not p. Williamson argues that this problem should be understood as a failure of luminosity, i.e., that if you are in a state then you are in a position to know that you are in that state. Williamson also argues that a version of deductive closure of knowledge is defensible as long as we drop the KK-principle. Since knowledge states aren’t luminous, standard arguments against closure don’t work. Colin Howson argues the subjective interpretation of the probability calculus should be understood in the framework of many-valued higher-order logics. Howson argues that the standard objections to second-order logic rely on a misguided conception of logic, and argues that we should instead concentrate on the model-theoretic notions of consistency and consequence. He then interprets the finitely additive probability calculus using these notions, linking fair bets with probabilities a la de Finetti. The restriction to finite additivity yields two logical properties: that a consistent probability assignment is extendable to a total assignment, and that an assignment is consistent if and only if all of its restrictions

Paired comparisons analysis: an axiomatic approach to ranking methods

In this paper we present an axiomatic analysis of several ranking methods for general tournaments. We find that the ranking method obtained by applying maximum likelihood to the (Zermelo-)Bradley-Terry model, the most common method in statistics and psychology, is one of the ranking methods that perform best with respect to the set of properties under consideration. A less known ranking method, generalised row sum, performs well too. We also study, among others, the fair bets ranking method, widely studied in social choice, and the least squares method.

Internal slackening scoring methods

We deal with the ranking problem of the nodes in a directed graph. The bilateral relationships specified by a directed graph may reflect the outcomes of a sport competition, the mutual reference structure between websites, or a group preference structure over alternatives. We introduce a class of scoring methods for directed graphs, indexed by a single nonnegative parameter α. This parameter reflects the internal slackening of a node within an underlying iterative process. The class of so-called internal slackening scoring methods, denoted by λα, consists of the limits of these processes. It is seen that λ0 extends the invariant scoring method, while λ∞ extends the fair bets scoring method. Method λ1 corresponds with the existing λ-scoring method of Borm et al. (Ann Oper Res 109(1):61–75, 2002) and can be seen as a compromise between λ0 and λ∞. In particular, an explicit proportionality relation between λα and λ1 is derived. Moreover, the internal slackening scoring methods are applied to the setting of social choice situations where they give rise to a class of social choice correspondences that refine both the Top cycle correspondence and the Uncovered set correspondence.

Bets on Hats: On Dutch Books Against Groups, Degrees of Belief as Betting Rates, and Group-Reflection

AbstractThe Story of the Hats is a puzzle in social epistemology. It describes a situation in which a group of rational agents with common priors and common goals seems vulnerable to a Dutch book if they are exposed to different information and make decisions independently. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. As it turns out, the Dutch book is flawed. It is based on the betting interpretation of the subjective probabilities, but ignores the fact that this interpretation disregards strategic considerations that might influence betting behavior. A lesson to be learned concerns the interpretation of probabilities in terms of fair bets and, more generally, the role of strategic considerations in epistemic contexts. Another lesson concerns Group-Reflection, which in its unrestricted form is highly counter-intuitive. We consider how this principle of social epistemology should be re-formulated so as to make it tenable.

Paired Comparisons Analysis: An Axiomatic Approach to Rankings in Tournaments

In this paper we present an axiomatic analysis of several ranking methods for tournaments. We find that two of them exhibit a very good behaviour with respect to the set of properties under consideration. One of them is the maximum likelihood ranking, the most common method in statistics and psychology. The other one is a new ranking method introduced in this paper: recursive Buchholz. One of the most widely studied methods in social choice, the fair bets ranking, also performs quite well, but fails to satisfy some arguably important properties.

Quantum mechanics with extended probabilities

The quantum mechanics of closed systems such as the universe is formulated using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for sets of alternative histories that are the basis of fair settleable bets. However, in quantum mechanics there are sets of alternative histories that can be described but which cannot be the basis for fair settleable bets. Members of such sets can be assigned extended probabilities that are sometimes negative. A prescription for extended probabilities is introduced that assigns extended probabilities to all histories that can be described, fine grained or coarse grained, members of decoherent sets or not. All probability sum rules are satisfied exactly. Sets of histories that are recorded to sufficient precision are the basis of settleable bets. This formulation is compared with the decoherent (consistent) histories formulation of quantum theory. Prospects are discussed for using this formulation to provide testable alternatives to quantum theory or further generalizations of it.

Fair Procedures: Evidence from Games Involving Lotteries

Procedures are the area where fairness arguably has its largest influence on modern societies. The experiments we report provide an initial characterisation of that influence and suggest new interpretations for some well‐known results. We find that procedural fairness is conceptually distinct from allocation fairness, although the evidence also indicates that the two are linked in important ways. Post hoc extension of one of the current models of fairness illustrates this link and implies that a deeper understanding of procedural fairness will require investigation of competing fairness norms. If a number of persons engage in a series of fair bets, the distribution of cash after the last bet is fair, or at least not unfair, whatever this distribution is. John Rawls (1971)

Narcissism, confidence, and risk attitude

AbstractThe present research addresses whether narcissists are more overconfident than others and whether this overconfidence leads to deficits in decision making. In Study 1, narcissism predicted overconfidence. This was attributable to narcissists' greater confidence despite no greater accuracy. In Study 2, participants were offered fair bets on their answers. Narcissists lost significantly more points in this betting task than non‐narcissists, due both to their greater overconfidence and greater willingness to bet. Finally, in Study 3, narcissists' predictions of future performance were based on performance expectations rather than actual performance. This research extends the literature on betting on knowledge to the important personality dimension of narcissism. Copyright © 2004 John Wiley & Sons, Ltd.

Fair bets and profitability in college football gambling

Efficient markets in college football are tested over a 25-year period, 1976–2000. the market in general is found to be efficient, but betting on underdogs of more than 28 points violates a fair bet. The strategy of betting home underdogs reveals stronger results. Home underdogs of more than seven points are found to reject the null hypotheses of a fair bet over the last 10 years of the sample, 1991–2000. Home underdogs of more than 28 points are found to reject the null of no profitability during the same time frame.

Efficient markets, fair bets, and profitability in NBA totals 1995–96 to 2001–02

The market for NBA totals was examined from 1995–96 to 2001–02. For the sample as a whole, a fair bet could not be rejected, leading to the conclusion of an efficient market. For the highest of the totals, however, the null hypothesis of a fair bet is rejected in the same manner as professional football in that overs are over bet. Although, winning percentages on betting the under above certain totals were found to be above 52.4%, the percentage needed to overcome the vigorish of the sportsbook, statistically significant violations of the null hypothesis of no profitability were not found. In addition, tests of betting with or against streaks in the spirit of the “hot hand” were not found to be profitable. It appears that bettors prefer the over to the under, but informed bettors will bet the under to the point where it is profitable for them to do so, which is enough to allow for the null hypothesis of a fair bet to be rejected, but not enough for profitability to be found.

New characterizations of the no-aging property and the ℓ1-isotropic model

The no-aging property and the ℓ1-isotropic model it implies have been introduced to overcome certain shortcomings of the exponential model. However, its definition is abstract and not very useful for practitioners. This paper presents several additional characterizations of the no-aging property. Included are (1) characterizations that appropriately generalize the memoryless property and the constant-failure-rate property of the exponential, (2) behavioral characterizations based on fair bets, and (3) geometric characterizations of the survival and density function and differential-geometric characterizations based on tensor methods.

New characterizations of the no-aging property and the ℓ1-isotropic model

The no-aging property and the ℓ1-isotropic model it implies have been introduced to overcome certain shortcomings of the exponential model. However, its definition is abstract and not very useful for practitioners. This paper presents several additional characterizations of the no-aging property. Included are (1) characterizations that appropriately generalize the memoryless property and the constant-failure-rate property of the exponential, (2) behavioral characterizations based on fair bets, and (3) geometric characterizations of the survival and density function and differential-geometric characterizations based on tensor methods.

The Evolution of Attitudes to Risk: Lottery Tickets and Relative Wealth

Individual attitudes to risk are examined in an evolutionary model. Males obtain more offspring as a consequence of greater wealth both directly and because this attracts more mates. The second effect induces gambling driven by relative wealth and can create Pareto inefficiency. Fair bets involving small losses and large gains are taken if any fair bets at all are taken. Altogether, the model accords with observations concerning bets taken and declined by typical individuals despite settings of widely varying per capita wealth.Journal of Economic LiteratureClassification Numbers: C72, D81.

The utility of art versus fair bets in the investment market

W~lliam Baumoi has shown convincingly that selection of a"good 9 " investment" in art is akin to placing a bet in a game of chance (Baumol, 1986). As is the case with most casinos, the odds favor the house. If compared to alternative investments, an art collection will yield less in capital gains. Baumol and others studied rates of return on purchases and sales at auction, that is, transactions in the tertiary art market, or the recycling market. This is, of course, the proper market to study, because only art traded in the major auction houses attains the required liquidity, which would make comparison with alternative assets realistic. However, most art is not bought in the tertiary market.

Fair Bets on Winners in Professional Golf

Fair Bets on Winners in Professional Golf

Beating the Spread: Testing the Efficiency of the Gambling Market for National Football League Games

In this paper we test the efficiency of the gambling market for National Football League games. Two efficiency tests are conducted. The first test is derived from the finance literature on market efficiency, while the second test is based on a market's being efficient when the rate of return on any gambling strategy based on publicly available information approximates the bookmaker's commission. While the first test is found to be too weak to establish conclusions about the efficiency of the NFL gambling market, the second test results, showing the existence of profitable betting opportunities, indicate that speculative inefficiencies exist in this market.

Abner Shimony. Coherence and the axioms of confirmation. The journal of symbolic logic, vol. 20 (1955), pp. 1–28. - R. Sherman Lehman. On confirmation and rational betting. The journal of symbolic logic, vol. 20 (1955), pp. 251–262. - John G. Kemeny. Fair bets and inductive probabilities. The journal of symbolic logic, vol. 20 (1955), pp. 263–273.

Abner Shimony. Coherence and the axioms of confirmation. The journal of symbolic logic, vol. 20 (1955), pp. 1–28. - R. Sherman Lehman. On confirmation and rational betting. The journal of symbolic logic, vol. 20 (1955), pp. 251–262. - John G. Kemeny. Fair bets and inductive probabilities. The journal of symbolic logic, vol. 20 (1955), pp. 263–273. - Volume 33 Issue 3

How to Survive a Fixed Number of Fair Bets

How to Survive a Fixed Number of Fair Bets