Our aim is to show how the well-known tale of Charles Perrault, Le Petit Poucet, contains the illustration of two principles of rational choice in a situation of uncertainty, the maximin ("to limit the breakage") and the maximax ("to target the best"). It builds in a targeted and economical way highly fluctuating situations which make inapplicable the first while showing the virtualities of the second principle. As such, this children's story has a new reading, which is not without connection (...) to the problem of the decisions of migrants in our troubled world. (shrink)

Voters satisfy maximin or maximax in their choices between sets of alternatives and secure a Pareto improvement by all voting strategically under simple majority voting for particular sincere preferences. Thus the assumption that strategic voting is a bad thing is challenged and the idea that we should reject voting because of the possibility of misrepresentation dismissed.

In this article, I address a controversial aspect of Rawls’s treatment of the question of justice between generations: how the parties in the original position could be motivated to select Rawls’s preferred principle of intergenerational savings, which he dubs the just savings principle. I focus on the explanation found in his later work, where he proposes that the correct savings principle is the principle that any generation would have wanted preceding generations to have followed. By expanding upon this explanation, I (...) respond to the objection that this explanation disregards the perspective of the first generation. I demonstrate that this objection ceases to be a concern when a proper account of the parties’ reasoning is developed. What is notable about the explanation I defend is that it relies on the parties adopting maximax – not maximin – as a rule for rational decision making. Having established this intermediary conclusion, I depart with Rawls and consider what savings principle the parties would choose if given more options. Ultimately, I argue that the parties would select a principle that Rawls would have undoubtedly rejected if presented to him at face value. This is because the principle of savings I argue would be selected requires continual economic growth over generations to increase upwards indefinitely – a conclusion Rawls is explicitly trying to avoid in his theory of justice. (shrink)

There has been much discussion on the two-envelope paradox. Clark and Shackel (2000) have proposed a solution to the paradox, which has been refuted by Meacham and Weisberg (2003). Surprisingly, however, the literature still contains no axiomatic justification for the claim that one should be indifferent between the two envelopes before opening one of them. According to Meacham and Weisberg, "decision theory does not rank swapping against sticking [before opening any envelope]" (p. 686). To fill this gap in the literature, (...) we present a simple axiomatic justification for indifference, avoiding any expectation reasoning, which is often considered problematic in infinite cases. Although the two-envelope paradox assumes an expectation-maximizing agent, we show that analogous paradoxes arise for agents using different decision principles such as maximin and maximax, and that our justification for indifference before opening applies here too. (shrink)

When someone hosts a party, when governments choose an aid program, or when assistive robots decide what meal to serve to a family, decision‐makers must determine how to help even when their recipients have very different preferences. Which combination of people’s desires should a decision‐maker serve? To provide a potential answer, we turned to psychology: What do people think is best when multiple people have different utilities over options? We developed a quantitative model of what people consider desirable behavior, characterizing (...) participants’ preferences by inferring which combination of “metrics” (maximax, maxsum, maximin, or inequality aversion [IA]) best explained participants’ decisions in a drink‐choosing task. We found that participants’ behavior was best described by the maximin metric, describing the desire to maximize the happiness of the worst‐off person, though participant behavior was also consistent with maximizing group utility (the maxsum metric) and the IA metric to a lesser extent. Participant behavior was consistent across variation in the agents involved and tended to become more maxsum‐oriented when participants were told they were players in the task (Experiment 1). In later experiments, participants maintained maximin behavior across multi‐step tasks rather than shortsightedly focusing on the individual steps therein (Experiment 2, Experiment 3). By repeatedly asking participants what choices they would hope for in an optimal, just decision‐maker, and carefully disambiguating which quantitative metrics describe these nuanced choices, we help constrain the space of what behavior we desire in leaders, artificial intelligence systems helping decision‐makers, and the assistive robots and decision‐makers of the future. (shrink)

This paper starts out from the proposition that case-based decision theory is an appropriate tool to explain human decision behavior in situations of structural ignorance. Although the developers of CBDT suggest its reality adequacy, CBDT has not yet been tested empirically very often, especially not in repetitive decision situations. Therefore, our main objective is to analyse the decision behavior of subjects in a repeated-choice experiment by comparing the explanation power of CBDT to reinforcement learning and to classical decision criteria under (...) uncertainty namely maximin, maximax, and pessimism-optimism. Our findings substantiate a predominant significantly higher validity of CBDT compared to the classical criteria and to reinforcement learning. For this reason, the experimental results confirm the suggested reality adequacy of CBDT in repetitive decision situations of structural ignorance. (shrink)

In a voting context, when the preferences of voters are described by linear orderings over a finite set of alternatives, the Maximin rule orders the alternatives according to their minimal rank in the voters’ preferences. It is equivalent to the Fallback bargaining process described by Brams and Kilgour (Group Decision and Negotiation 10:287–316, 2001). This article proposes a characterization of the Maximin rule as a social welfare function (SWF) based upon five conditions: Neutrality, Duplication, Unanimity, Top Invariance, and Weak Separability. (...) In a similar way, we obtain a characterization for the Maximax SWF by using Bottom Invariance instead of Top Invariance. Then, these results are compared to the axiomatic characterizations of two famous scoring rules, the Plurality rule and the Antiplurality rule. (shrink)

In 1980, Amartya Sen’s essay ‘Equality of What?’ stimulated a still ongoing discussion on the question: ‘Insofar as one holds that social justice demands rendering people’s condition more nearly equal, what aspects of people’s condition should be equalized?’ (Sen, 1982). In what respects should people be rendered more nearly the same? Prominent responses include resources, fundamental liberties, capabilities, advantages, welfare, and opportunities for welfare.1 There is a more general question in this neighbourhood that should be of interest. We might conceive (...) of social justice as requiring us to maximize some function of some aspect of people’s condition. The relevant aspect might be any of the candidates just listed or some hitherto unnoticed alternative. But it is not obvious in advance of argument that social justice requires equality of any sort. Perhaps the function we should be maximizing requires us to equalize, but it might be ‘maximize the average!’, ‘maximize the aggregate!’, ‘maximin!’, ‘equalize at the highest feasible level!’, ‘maximax!’, ‘prioritize!’, ‘maximize the number above sufficiency!’, or yet another alternative. The more general question about the nature of social justice requirements is ‘Whatever of what?’ There are two issues to resolve, not just one. (shrink)

Two of the most poignant decisions in pediatrics concern disagreements between physicians and families over imperiled newborns. When can the family demand more life-sustaining treatment than physicians want to provide? When can it properly ask for less? The author looks at these questions from the point of view of decision theory, and first argues that insofar as the family acts in the child’s best interest, its choices cannot be constrained, and that the maximax and minimax strategies are equally in (...) the child’s best interest. He then proposes a guideline according to which the family can demand LST if it is physiologically possible to preserve a life the child can be expected to welcome, and refuse such treatment if it causes suffering that is “more than can be borne” even if an uncompromised life is expected to emerge. (shrink)

The purpose of the article is to draw comparisons between the major normative rules of distributive justice. This comparison is based on a kind of distribution of goods which is sometimes called the problem of pure distribution, i.e. the distribution of a homogeneous, infinitely distributable good in a situation when claims of different persons on the distributed good were in no way differentiated. This problem is defined against the background of typology of problems of goods distribution. Normative rules of distributive (...) Justice are defined formally as social welfare functionals. Eight rules of justice are distinguished: the rule of the utilitarian, Rawls’s maximin rule, Rawls’s lexicographical maximin rule, the maximax rule of the conservatives, the rule of lexicographical maximax of the conservatives, Nash’s rule, and two rules advanced by egalitarianists which differ by the meaning attributed to equality of distribution. Premises underlying the construction of these rules of justice and which indicate the measurement of preferences and possibilities of interpersonal comparisons are discussed. The same justice rules are also presented graphically. The method of the comparison amounts to examining if a certain set of ethical postulates is fulfilled by the rules under consideration. Several ethical postulates concerning the distribution of goods are formulated. Some of them define conditions any method of evaluating inequality of distribution of goods should fulfil. The remaining postulates involve more general requirements put to methods of making social decisions. Theorems about the fulfilment or nonfulfilment by individual rules of distributive justice of the considered ethical postulates are presented in a recapitulating table. The author demonstrates that almost a1l justice rules fulfil general postulates put to methods of social decision making. Nash’s rule and the two rules of the egalitarians are the exceptions, as they do not fulfil the postulate of separability with respect to unconcerned individuals. Besides, the two rules of the egalitarians do not fulfil the Pareto optimality principle. Significant differences between rules of distributive justice become manifest only when you compare way they fulfil ethical postulates concerning the manner of evaluating the inequality of the distribution. With regard to this set of postulates, they can be arranged along a definite continuum, with Rawls’s lexicographical maximin — the radical egalitarian rule, and the lexicographical maximax of the conservatives – the radical conservative rule as the extreme points of this continuum. (shrink)

It would be improper for a President to play safe. After two years of curbing my tongue and not making all sorts of observations that have sprung to my mind, in order to let you have an opportunity of having your say, I am now off the leash. And whereas mostly in academic life it is appropriate to adopt a prudential strategy, and not say anything that might be wrong, I owe it to you on this occasion to play a (...) maximax strategy, to speak out and say what I really think, being willing to run the risk of being wrong in order not to forgo the chance of actually being right in an area of the philosophy of science which must, I think for ever, be largely a matter of metaphysical speculation. (shrink)

A substantial body of empirical evidence shows that individuals overweight extreme events and act in conflict with the expected utility theory. These findings were the primary motivation behind the development of a rank-dependent utility theory for choice under uncertainty. The purpose of this paper is to demonstrate that some simple empirical rules of thumb for choice under uncertainty are consistent with the rank-dependent utility theory.