Open questions in utility theory

Throughout this paper, our main idea is to explore different classical questions arising in Utility Theory, with a particular attention to those that lean on numerical representations of preference orderings. We intend to present a survey of open questions in that discipline, also showing the state-of-art of the corresponding literature.This work is partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), and TIN2016-77356-P (MINECO/ AEI-FEDER, UE)

Voting power measurement: a story of misreinvention

In this account of the history of voting-power measurement, we confine ourselves to the concept of a priori voting power. We show how the concept was re-invented several times and how the circumstances in which it was reinvented led to conceptual confusion as to the true meaning of what is being measured. In particular, power-as-influence was conflated with value in the sense of transferable utility cooperative game theory (power as share in constant total payoff). Influence was treated, improperly, as though it were transferable utility, and hence an additive and distributive quantity. We provide examples of the resulting misunderstanding and mis-directed criticism

Dissection of Pol II Trigger Loop Function and Pol II Activity–Dependent Control of Start Site Selection In Vivo

Structural and biochemical studies have revealed the importance of a conserved, mobile domain of RNA Polymerase II (Pol II), the Trigger Loop (TL), in substrate selection and catalysis. The relative contributions of different residues within the TL to Pol II function and how Pol II activity defects correlate with gene expression alteration in vivo are unknown. Using Saccharomyces cerevisiae Pol II as a model, we uncover complex genetic relationships between mutated TL residues by combinatorial analysis of multiply substituted TL variants. We show that in vitro biochemical activity is highly predictive of in vivo transcription phenotypes, suggesting direct relationships between phenotypes and Pol II activity. Interestingly, while multiple TL residues function together to promote proper transcription, individual residues can be separated into distinct functional classes likely relevant to the TL mechanism. In vivo, Pol II activity defects disrupt regulation of the GTP-sensitive IMD2 gene, explaining sensitivities to GTP-production inhibitors, but contrasting with commonly cited models for this sensitivity in the literature. Our data provide support for an existing model whereby Pol II transcriptional activity provides a proxy for direct sensing of NTP levels in vivo leading to IMD2 activation. Finally, we connect Pol II activity to transcription start site selection in vivo, implicating the Pol II active site and transcription itself as a driver for start site scanning, contravening current models for this process