Why bayesian “evidence for H1” in one condition and bayesian “evidence for H0” in another condition does not mean good-enough bayesian evidence for a difference between the conditions

Psychologists are often interested in whether an independent variable has a different effect in condition A than in condition B. To test such a question, one needs to directly compare the effect of that variable in the two conditions (i.e., test the interaction). Yet many researchers tend to stop when they find a significant test in one condition and a nonsignificant test in the other condition, deeming this as sufficient evidence for a difference between the two conditions. In this Tutorial, we aim to raise awareness of this inferential mistake when Bayes factors are used with conventional cutoffs to draw conclusions. For instance, some researchers might falsely conclude that there must be good-enough evidence for the interaction if they find good-enough Bayesian evidence for the alternative hypothesis, H1, in condition A and good-enough Bayesian evidence for the null hypothesis, H0, in condition B. The case study we introduce highlights that ignoring the test of the interaction can lead to unjustified conclusions and demonstrates that the principle that any assertion about the existence of an interaction necessitates the direct comparison of the conditions is as true for Bayesian as it is for frequentist statistics. We provide an R script of the analyses of the case study and a Shiny app that can be used with a 2 × 2 design to develop intuitions on this issue, and we introduce a rule of thumb with which one can estimate the sample size one might need to have a well-powered design

A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market

We present the first combinatorial polynomial time algorithm for computing the equilibrium of the Arrow-Debreu market model with linear utilities.Comment: Preliminary version in ICALP 201

Statistical Curse of the Second Half Rank

In competitions involving many participants running many races the final rank is determined by the score of each participant, obtained by adding its ranks in each individual race. The "Statistical Curse of the Second Half Rank" is the observation that if the score of a participant is even modestly worse than the middle score, then its final rank will be much worse (that is, much further away from the middle rank) than might have been expected. We give an explanation of this effect for the case of a large number of races using the Central Limit Theorem. We present exact quantitative results in this limit and demonstrate that the score probability distribution will be gaussian with scores packing near the center. We also derive the final rank probability distribution for the case of two races and we present some exact formulae verified by numerical simulations for the case of three races. The variant in which the worst result of each boat is dropped from its final score is also analyzed and solved for the case of two races.Comment: 16 pages, 10 figure

Axiomatic Characterization of the Mean Function on Trees

A mean of a sequence π = (x1, x2, . . . , xk) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean(π) = { x | x is a mean of π } is called the mean function on X. In this paper the mean function on finite trees is characterized axiomatically

Utilitarian Collective Choice and Voting

In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow’s theorem, all voting methods must be seriously flawed. Arrow’s theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow’s result. Parallel to Arrow’s ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow’s theorem, but rather from restrictions imposed on voters’ expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 logM) time (where M is the number of social outcomes).Comment: 42 pages, 4 figures, 8 tables, 1 algorithm

Adaptive Investment Strategies For Periodic Environments

In this paper, we present an adaptive investment strategy for environments with periodic returns on investment. In our approach, we consider an investment model where the agent decides at every time step the proportion of wealth to invest in a risky asset, keeping the rest of the budget in a risk-free asset. Every investment is evaluated in the market via a stylized return on investment function (RoI), which is modeled by a stochastic process with unknown periodicities and levels of noise. For comparison reasons, we present two reference strategies which represent the case of agents with zero-knowledge and complete-knowledge of the dynamics of the returns. We consider also an investment strategy based on technical analysis to forecast the next return by fitting a trend line to previous received returns. To account for the performance of the different strategies, we perform some computer experiments to calculate the average budget that can be obtained with them over a certain number of time steps. To assure for fair comparisons, we first tune the parameters of each strategy. Afterwards, we compare the performance of these strategies for RoIs with different periodicities and levels of noise.Comment: Paper submitted to Advances in Complex Systems (November, 2007) 22 pages, 9 figure

Boolean delay equations on networks: An application to economic damage propagation

We introduce economic models based on Boolean Delay Equations: this formalism makes easier to take into account the complexity of the interactions between firms and is particularly appropriate for studying the propagation of an initial damage due to a catastrophe. Here we concentrate on simple cases, which allow to understand the effects of multiple concurrent production paths as well as the presence of stochasticity in the path time lengths or in the network structure. In absence of flexibility, the shortening of production of a single firm in an isolated network with multiple connections usually ends up by attaining a finite fraction of the firms or the whole economy, whereas the interactions with the outside allow a partial recovering of the activity, giving rise to periodic solutions with waves of damage which propagate across the structure. The damage propagation speed is strongly dependent upon the topology. The existence of multiple concurrent production paths does not necessarily imply a slowing down of the propagation, which can be as fast as the shortest path.Comment: Latex, 52 pages with 22 eps figure

Behavioral implications of shortlisting procedures

We consider two-stage “shortlisting procedures” in which the menu of alternatives is first pruned by some process or criterion and then a binary relation is maximized. Given a particular first-stage process, our main result supplies a necessary and sufficient condition for choice data to be consistent with a procedure in the designated class. This result applies to any class of procedures with a certain lattice structure, including the cases of “consideration filters,” “satisficing with salience effects,” and “rational shortlist methods.” The theory avoids background assumptions made for mathematical convenience; in this and other respects following Richter’s classical analysis of preference-maximizing choice in the absence of shortlisting

Trust and control interrelations: New perspectives on the trust control nexus

This article is the post-print version of the published article that may be accessed at the link below. Copyright @ 2007 Sage Publications.This article introduces the special issue on New Perspectives on the Trust-Control Nexus in Organizational Relations. Trust and control are interlinked processes commonly seen as key to reach effectiveness in inter- and intraorganizational relations. The relation between trust and control is, however, a complex one, and research into this relation has given rise to various and contradictory interpretations of how trust and control relate. A well-known discussion is directed at whether trust and control are better conceived as substitutes, or as complementary mechanisms of governance. The articles in this special issue bring the discussion on the relationship between both concepts a step further by identifying common factors, distinctive mechanisms, and key implications relevant for theory building and empirical research. By studying trust and control through different perspectives and at different levels of analysis, the articles provide new theoretical insights and empirical evidence on the foundations of the trust-control interrelations