A simple test of Richter-rationality

We propose in this note a simple non-parametric test of Richter-rationality which is the basic definition of rationality used in choice functions theory. Loosely speaking, the data set is rationalizable in the Richter' sense if there exists a complete-acyclic binary relation that rationalizes the data set. Hence a data set is rationalizable in the Richter' sense if there exists a variable intervals function which rationalizes this data set. Since an acyclic binary relation is not necessary transitive then the proposed Richter-rationality test is weaker than GARP. Finally the test is performed over Mattei's data sets.GARP ; choice functions ; Richter-rationality ; variable intervals functions.

Biased quantitative measurement of interval ordered homothetic preferences

We represent interval ordered homothetic preferences with a quantitative homothetic utility function and a multiplicative bias. When preferences are weakly ordered (i.e. when indifference is transitive), such a bias equals 1. When indifference is intransitive, the biasing factor is a positive function smaller than 1 and measures a threshold of indifference. We show that the bias is constant if and only if preferences are semiordered, and we identify conditions ensuring a linear utility function. We illustrate our approach with indifference sets on a two dimensional commodity space.Weak order, semiorder, interval order, intransitive indifference, independence, homothetic, representation, linear utility

Interval orders and reverse mathematics

We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain $2 \oplus 2$. We also study proper interval orders and their characterization theorem: a partial order is a proper interval order if and only if it contains neither $2 \oplus 2$ nor $3 \oplus 1$.Comment: 21 pages; to appear in Notre Dame Journal of Formal Logic; minor changes from the previous versio

Some two-process models for memory

Two-process models for memory and learnin

Paradoxes of two-length interval orders

AbstractA two-length interval order is a partially ordered set whose points can be mapped into closed real intervals such that (i) the interval for x lies wholly to the right of the interval for y if and only if x is ranked above y in the partial ordering, and (ii) only two different lengths are involved in the mapping. With the shorter length fixed at 1, let L denote the set of admissible longer lengths for which (i) and (ii) hold for a given interval order.The paper demonstrates that there are two-length interval orders on finite point sets with the following L sets for each integer m⩾2: L = (1,m); L = (2−1m, 2)∪(m,∞); L = (m,2m− 1)∪(2m−1,∞). The second case shows that L can have an arbitrarily big gap between admissible longer lengths, and the third case leads to the corollary that there can be arbitrarily many gaps or holes in L