A formulation of the determinism hypothesis

The author tries to formulate what a determinist believes to be true. The formulation is based on some concepts defined in a systems-theoretical manner, mainly on the concept of an experiment over the sets A ^m (a set of m-tuples of input values) and B ⁿ (a set of n-tuples of output values) in the time interval (t ₁, ..., t _k ) (symbolically E[t ₁,..., t _k , A ^m , B ⁿ ]), on the concept of a behavior of the system S ^m,n (=(A ^m , B ⁿ )) on the basis of the experiment E[t ₁, ..., t _k , A ^m , B ⁿ ] and, indeed, on the concept of deterministic behavior .... The resulting formulation of the deterministic hypothesis shows that this hypothesis expresses a belief that we always could find some hidden parameters.     

A Shortcut Method of Calculating the Distribution of Election Outcome Types Under Approval Voting

The paper applies to approval voting, under which the voter casts a ballot by casting one vote for each of k candidates, wherek=;1,2, , m–1 and there are m candidates. I assume (following Brams and Fishburn) that each of the voter's 2=;–2 strategies is equally likely to be chosen. Election-outcome types include: the m-way tie;(m-1) -way ties with the runner-up trailing by 1,2,,m votes; (m-2)-way ties, and so on. The frequency distribution of outcome types varies only with m and n and is necessary to the calculation of the expected utilities of successive ballots cast, in the same election, by a voter under a variant of approval voting. This variant allows the voter to cast several complete ballots provided that he pays the respective prices, which could reasonably be based on the expected utilities. The paper describes a shortcut method of calculating the distribution of outcome types when m=;4 andn rises to levels that make straightforward calculation computationally infeasible. The shortcut involves the combining of an outcome type, instead of each member of that type, with each of the 14 strategies available to the incremental voter. In going fromn-1 to n, for n3, the number of outcome types increases by a factor of (n+3)/n whereas, the number of combinations of strategies increases by a factor of 14.     

Consensus By Identifying Extremists

Given a finite state space and common priors, common knowledge of the identity of an agent with the minimal (or maximal) expectation of a random variable implies consensus, i.e., common knowledge of common expectations. This extremist statistic induces consensus when repeatedly announced, and yet, with n agents, requires at most log₂ n bits to broadcast.     

Domination structures and multicriteria problems in n-person games

Multiple criteria decision problems with one decision maker have been recognized and discussed in the recent literature in optimization theory, operations research and management science. The corresponding concept with n-decision makers, namely multicriteria n-person games, has not yet been extensively explored.In this paper we first demonstrate that existing solution concepts for single criterion n-person games in both normal form and characteristic function form induce domination structures (similar to those defined and studied by Yu [39] for multicriteria single decision maker problems) in various spaces, including the payoff space, the imputation space and the coalition space. This discussion provides an understanding of some underlying assumptions of the solution concepts and provides a basis for generalizing and generating new solution concepts not yet defined. Also we illustrate that domination structures may be regarded as a measure of power held by the players.We then illustrate that a multicriteria problem can naturally arise in decision situations involving (partial) conflict among n-persons. Using our discussion of solution concepts for single criterion games as a basis, various approaches for resolving both normal form and characteristic function form multicriteria n-person games are proposed. For multicriteria games in characteristic function form, we define a multicriteria core and show that there exists a single game point whose core is equal to the multicriteria core. If we reduce a multicriteria game to a single criterion game, domination structures which are more general than classical ones must be considered, otherwise some crucial information in the game may be lost. Finally, we discuss a parametrization process which, for a given multicriteria game, associates a single criterion game to each point in a parametric space. This parametrization provides a basis for the discussion of solution concepts in multicriteria n-person games.     

Sophisticated Voting Under the Sequential Voting by Veto1

The research reported here was the first empirical examination of strategic voting under the Sequential Voting by Veto (SVV) voting procedure, proposed by Mueller (1978). According to this procedure, a sequence of n voters must select s out of s+m alternatives (mn2; s>0). Hence, the number of alternatives exceeds the number of participants by one (n+1). When the ith voter casts her vote, she vetoes the alternative against which a veto has not yet been cast, and the s remaining non-vetoed alternatives are elected. The SVV procedure invokes the minority principle, and it has advantages over all majoritarian procedures; this makes SVV a very desirable means for relatively small groups to make collective decisions. Felsenthal and Machover (1992) pointed out three models of voting under SVV: sincere, optimal, and canonical. The current research investigated, through laboratory experiments, which cognitive model better accounts for the voters' observed behavior and the likelihood of obtaining the optimal outcome as a function of the size of n (when s=1). The findings suggest that while voters under SVV use all three models, their choice is conditioned by group size. In the small groups (n=3), the canonical mode was a better predictor than the sincere model. In the larger groups (n=5), the sincere model was a better predictor than the canonical model. There is also evidence of players' learning during the experiment.     

Endogenous risk and protection premiums

Endogenous risk implies an individual perceives he can influence the likelihood that a state of nature will occur. To add structure to endogenous risk models, I define a protection premium for reduced uncertainty about protection efficiency when a stochastic variable enters the probability functionp(x) rather than the utility function. For a binary lottery, a measure of aversion of uncertain protection efficiency(x) =-p(x)/p(x) is defined to unambiguously determine the effects of increased risk on an individual's voluntary contribution to public good supply earmarked to reduce the probability of an undesirable state. Finally, I examine the protection premium in ann-state discrete lottery and when uncertainty exists in both the probability and utility function.     

Sequential voting by veto: Making the Mueller-Moulin algorithm more versatile

This paper shows that a relatively easy algorithm for computing the (unique) outcome of a sophisticated voting procedure called sequential voting by veto (SVV) applies to a more general situation than considered hitherto. According to this procedure a sequence of n voters must select s out of m + s options (s > 0, m 3 n 3 2). The ith voter, when his turn comes, vetoes k _i options (k _i 1, k _i = m). The s remaining non-vetoed options are selected. Every voter is assumed to be fully informed of all other voters total (linear) preference orderings among the competing options, as well as of the order in which the veto votes are cast. This algorithm was proposed by Mueller (1978) for the special case where s and the k _i are all equal to 1, and extended by Moulin (1983) to the somewhat more general case where the k _i are arbitrary but s is still 1. Some theoretical and practical issues of voting by veto are discussed.     

Challenges of Dealing with Financial Concerns during Life-Threatening Illness: Perspectives of Health Care Practitioners

ABSTRACT

The costs of serious medical illness and end of life care are often a heavy burden for patients and families (Collins, Stepanczuk, Williams, & Rich, 2016 Collins, A., Stepanczuk, C., Williams, N., & Rich, E. (2016). Supporting better patient decisions at the point of care: What payers and delivery systems can do (Mathematica Policy Research Issue Brief). Retrieved from http://econpapers.repec.org/paper/mprmprres/6c6a86e28d7149c993713352eeceaa18.htm [Google Scholar]; Kim, 2007 Kim, P. (2007). Cost of cancer care: The patient perspective. Journal of Clinical Oncology, 25(2), 228–232. doi:10.1200/JCO.2006.07.9111[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; May et al., 2014 May, C. R., Eton, D. T., Boehmer, K., Gallacher, K., Hunt, K., MacDonald, S.,?… &?Rogers, A. E. (2014). Rethinking the patient: Using burden of treatment theory to understand the changing dynamics of illness. BMC health services research, 14(1), 1–11. doi:10.1186/1472-6963-14-281[Crossref], [PubMed] , [Google Scholar]; Zarit, 2004 Zarit, S. H. (2004). Family care and burden at the end of life. Canadian Medical Association Journal, 170(12), 1811–1812. doi:10.1503/cmaj.1040196[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Twenty-six practitioners, including social workers, managers/administrators, supervisors, and case managers from five health care settings, participated in qualitative semistructured interviews about financial challenges patients encountered. Seven practitioners took part in a focus group. Practitioners were recruited from hospice (n?=?5), long-term care (n?=?5), intensive care (n?=?5), dialysis (n?=?6), and oncology (n?=?5). Interview and focus group questions focused on financial challenges patients encountered when facing life-threatening illness. Interview data were transcribed and thematically coded and trustworthiness of data was established with peer debriefing, member checking, and agreement on themes among the authors. Practitioners described interacting micro, meso, and macroinfluences on the financial well-being and challenges patients encountered. Microlevel influences involved patient characteristics, such as their demographic profile and/or health status that set them up for financial aptitude or challenges. Macrolevel influences involved the larger health care/safety net system, which provided valuable resources for some patients but not others. Practitioners also discussed the mesolevel of influence, the local setting where they worked to match available resources with patients’ individual needs given the constraints emerging from the micro and macrolevels. Practitioners described how they navigated the interplay of these three areas to meet patients’ needs and cope with financial challenges. Implications for practice point to directly addressing the kind of financial concerns that patients and families facing financial burden from serious medical illness have, and identifying ways to bridge knowledge and resource access gaps at the individual, organizational, and societal levels.     

Echelons in Incomplete Relations

An efficient method of value assessment of a set of exchangeable alternatives A = {a ₁,a ₂, ,a _n} is presented. It particularly applies to situations where certain preferences may be easily evaluated or are already known, while other binary comparisons may not at once be available. Further applications are to ranking partial tournaments and the emergence and the characterisation of organisational hierarchy. By sequentially performing transitively efficient assessments of uncompared pairs, an initial weakly acyclical preference structure in A is transformed into an ordering of A in echelons. We call these nicely surveyable preference structures echelon orders. Theoretical properties of echelon orders are investigated, including a characterisation and a numerical representation.     

Game-theoretic analyses of coalition behavior

Coalitions are frequently more visible than payoffs. The theory of n-person games seeks primarily to identify stable allocations of valued resources; consequently, it gives inadequate attention to predicting which coalitions form. This paper explores a way of correcting this deficiency of game-theoretic reasoning by extending the theory of two-person cooperative games to predict both coalitions and payoffs in a three-person game of status in which each player seeks to maximize the rank of his total score. To accomplish this, we analyze the negotiations within each potential two-person coalition from the perspective of Nash's procedure for arbitrating two-person bargaining games, then assume that players expect to achieve the arbitrated outcome selected by this procedure and use these expectations to predict achieved ranks and to identify players' preferences between alternative coalition partners in order to predict the probability that each coalition forms. We test these payoff and coalition predictions with data from three laboratory studies, and compare the results with those attained in the same data by von Neumann and Morgenstern's solution of two-person cooperative games, Aumann and Maschler's bargaining set solution for cooperative n-person games, and an alternative model of coalition behavior in three-person sequential games of status.

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Games,goals, and bounded rationality

A generalization of the standard n-person game is presented, with flexible information requirements suitable for players constrained by certain types of bounded rationality. Strategies (complete contingency plans) are replaced by policies, i.e., endmean pairs of goals and controls (partial contingency plans), which results in naturally disconnected player choice sets. Well-known existence theorems for pure strategy Nash equilibrium and bargaining solutions are generalized to policy games by modifying connectedness (convexity) requirements.     

Comparative accuracy of value solutions in non-sidepayment games with empty core

This article reports a test of the predictive accuracy of solution concepts in cooperative non-sidepayment n-person games with empty core. Six solutions were tested. Three of these were value solutions (i.e., -transfer value, -transfer nucleolus, and -transfer disruption value) and three were equilibrium solutions (deterrence set, stable set, and imputation set). The test was based on a laboratory experiment utilizing 5-person, 2-choice normal form games with empty core; other related data sets were also analyzed. Goodness-of-fit results based on discrepancy scores show that the three value solutions are about equally accurate in predicting outcomes, and that all three are substantially more accurate than the other solutions tested.     

Predictive superiority of the beta-characteristic function in cooperative non-sidepayment N-person games

This article reports an experimental study of decision-making outcomes in cooperative non-sidepayment games. The objective of this test was to determine which characteristic function, V (S) or V (S), provides the most accurate basis for payoff predictions from solution concepts. The experiment tested three solution concepts (core, stable set, imputation set) in the context of 5-person, 2-strategy non-sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both V (S) and V (S), making a total of six predictive theories under test. Consistent with earlier studies (Michener et al., 1984a; Michener et al., 1985), two basic findings emerged. First, the data show that for each of the solutions tested, the prediction from any solution concept computed from V(S) was more accurate than the prediction from the same solution concept computed from V (S). Second, the -core was the most accurate of the six theories tested. Overall, these results support the view that V (S) is superior to V (S) as a basis for payoff predictions in cooperative non-sidepayment games.     

The general relevance of the impossibility teorem in smooth social choice

A complete classification theorem for voting processes on a smooth choice spaceW of dimensionw is presented. Any voting process is classified by two integersv ^* () andw(), in terms of the existence or otherwise of the optima set, IO(), and the cycle set IC().In dimension belowv ^* () the cycle set is always empty, and in dimension abovew() the optima set is nearly always empty while the cycle set is open dense and path con nected. In the latter case agenda manipulation results in any outcome.For admissible (compact, convex) choice spaces, the two sets are related by the general equilibrium result that IO() union IC() is non-empty. This in turn implies existence of optima in low dimensions. The equilibrium theorem is used to examine voting games with an infinite electorate, and the nature ofstructure induced equilibria, induced by jurisdictional restrictions.This material is based on work supported by a Nuffield Foundation grant.     

Inferring a linear ordering over a power set

An observer attempts to infer the unobserved ranking of two ideal objects, A and B, from observed rankings in which these objects are `accompanied' by `noise' components, C and D. In the first ranking, A is accompanied by C and B is accompanied by D, while in the second ranking, A is accompanied by D and B is accompanied by C. In both rankings, noisy-A is ranked above noisy-B. The observer infers that ideal-A is ranked above ideal-B. This commonly used inference rule is formalized for the case in which A,B,C,D are sets. Let X be a finite set and let be a linear ordering on 2^X. The following condition is imposed on . For every quadruple (A,B,C,D)Y, where Y is some domain in (2^X)⁴, if and , then . The implications and interpretation of this condition for various domains Y are discussed.     

On inference from inconsistent premisses

The main object of this paper is to provide the logical machinery needed for a viable basis for talking of the consequences, the content, or of equivalences between inconsistent sets of premisses.With reference to its maximal consistent subsets (m.c.s.), two kinds of consequences of a propositional set S are defined. A proposition P is a weak consequence (W-consequence) of S if it is a logical consequence of at least one m.c.s. of S, and P is an inevitable consequence (I-consequence) of S if it is a logical consequence of all the m.c.s. of S. The set of W-consequences of a set S it determines (up to logical equivalence) its m.c.s. (This enables us to define a normal form for every set such that any two sets having the same W-consequences have the same normal form.) The W-consequences and I-consequences will not do to define the content of a set S. The first is too broad, may include propositions mutually inconsistent, the second is too narrow. A via media between these concepts is accordingly defined: P is a P-consequence of S, where P is some preference criterion yielding some of the m.c.s. of S as preferred to others, and P is a consequence of all of the P-preferred m.c.s. of S. The bulk of the paper is devoted to discussion of various preference criteria, and also surveys the application of this machinery in diverse contexts - for example, in connection with the processing of mutually inconsistent reports.     

Changes in preference

A basic framework for studies of changes in preference is introduced, and four types of changes in preference are identified.Revision by a sentence such as A is better thanB means that a preference forA overB is acquired. The result ofcontraction by A is better thanB is that the subject no longer holdsA to be better thanB. Inaddition andsubtraction, an alternative is added to, or subtracted from, respectively, the set of alternatives that are under consideration. Formal models of these four types of change are introduced, and they are shown to satisfy plausible postulates for rational changes in preferences.     

When an Event Makes a Difference

For (S, Σ) a measurable space, let and be convex, weak^* closed sets of probability measures on Σ. We show that if ∪ satisfies the Lyapunov property , then there exists a set A ∈ Σ such that min_μ1∈ μ₁(A) > max_μ2 ∈ (A). We give applications to Maxmin Expected Utility (MEU) and to the core of a lower probability.     

Signed orders in linear and nonlinear utility theory

Self-reflecting signed orders on a set A and its anti-set A ^* were introduced previously as a way to account for negative as well as positive feelings about the inclusion of items in A in potential subsets of choice. The present paper extends the notion of signed orders to lotteries on A A ^*, describes reflection axioms for the lottery context, and shows how these axioms simplify utility representations for preference between lotteries. The simplified representations are then used to guide procedures for extending preferences from A A ^* and its lotteries to preferences between subsets of items.     

Reasonable beliefs

The theory of inductive inference developed by I. Levi in Gambling with Truth has two important limitations. In the first place, it makes acceptability of hypotheses question-dependent: any statement of the form It is reasonable to believe a hypothesis h on evidence e has to be expanded so as to include a reference to some specific question which h is supposed to answer, or, alternatively, to a set of possible answers which is associated with that question. Secondly, Levi's account is insensitive to modal distinctions: no difference is made between what is merely reasonable to believe and what is unreasonable not to believe. The aim of this paper is to construct a theory which utilizes Levi's main proposals and, at the same time, avoids the above-mentioned limitations.