Regardless of their name (dictionary, glossary, encyclopaedia, or even ‘leximat’, in the case of a new generation of online, semi-automated lexicographic tools), subject-field, purpose, or medium (paper or cyber), lexicographic reference works should be regarded as functional information tools that are solely designed to cater to the information needs of their users in different usage situation...

Let I be a homogeneous Artinian ideal in a polynomial ring R = k[x1, . . . , xn] over a field k of characteristic 0. We study an equivalent condition for the generic initial ideal gin(I) with respect to reverse lexicographic order to be almost reverse lexicographic. As a result, we show that Moreno-Socias conjecture implies Fröberg conjecture. And for the case codimI ≤ 3, we show that R/I has t...

This paper presents three simple and efficient algorithms for generating, ranking and unranking t-ary trees in a lexicographic order. The simplest idea of encoding a t-ary tree with n nodes as a bit-string of length t*n is exploited to its full advantages. It is proved that the lexicographic order in the set of t-ary trees with n nodes is preserved in the set of bit-strings of length t*n, using...

We interpret the problem of updating beliefs as a choice problem (selecting a posterior from a set of admissible posteriors) with a reference point (prior). We use AGM belief revision to define the support of admissible posteriors after observing zero probability events and investigate two classes of updating rules for probabilities : 1) ”minimum distance” updating rules which select the poster...

We propose a model, Lexicographic Partially Observable Markov Decision Process (LPOMDP), which extends POMDPs with lexicographic preferences over multiple value functions. It allows for slack–slightly less-than-optimal values–for higherpriority preferences to facilitate improvement in lower-priority value functions. Many real life situations are naturally captured by LPOMDPs with slack. We cons...

We consider cheap talk by a biased expert comparing multiple issues, e.g., discussion of different spending proposals by an industry lobbyist, evaluation of different stocks by a sell-side analyst, or analysis of different topics by a biased newspaper. When the expert’s motives are sufficiently transparent, we find that cheap talk is credible and influential even when the expert strongly favors...

We study the problem of elicitation of subjective beliefs of an agent when the beliefs are ambiguous (the set of beliefs is a non-singleton set) and the agent’s preference exhibits ambiguity aversion; in particular, as represented by α-maxmin preferences. We construct a direct revelation mechanism such that truthful reporting of beliefs is the agent’s unique best response. The mechanism uses kn...

This paper examines the nature of partisan preferences on a range of issue scales. It compares preferences in a period of strong ideological focus, in the late eighties and early nineties, with preferences in 2000 and 2001 – a period of weak ideological focus. Where partisan preferences were formerly polarised, they are now more consensual. I argue that once positional issues now resemble valen...