arXiv subjects

Geoffrey Pritchard

Publications and source records attributed to Geoffrey Pritchard.

10 recordsLinked to original sources

arXiv2026

The Value of Perfect Endpoint Forecasts for Offshore-Wind Thermal Firming

Forecast value depends not only on accuracy but also on the information structure available to the operating model. We study a diagnostic current-endpoint-only forecast for offshore-wind thermal firming: at hour t, the controller observes the current net-demand state z_t and one perfect future target z_{t+h}, but not the intermediate path or earlier endpoint messages. Unlike rolling path forecasts, these endpoint information sets are not nested in h. We embed the signal in a cyclostationary MDP using quantile Fourier regression states estimated from ISO New England load and offshore wind data, and solve annual state-action-frequency LPs for h = 1, . . . , 6. A one-hour endpoint forecast reduces annual firming cost by 8.07%, while a six-hour endpoint reduces it by 2.28%. The decreasing profile shows that a single farther endpoint is less actionable for a one-step ramping decision, without implying that longer rolling forecasts are less valuable.

math.OC↗

arXiv2026

Risk-Averse Markov Decision Processes: Applications to Electricity Grid and Reservoir Management

This paper develops risk-averse models to support system operators in planning and operating the electricity grid under uncertainty from renewable power generation. We incorporate financial risk hedging using conditional value at risk (CVaR) within a Markov Decision Process (MDP) framework and propose efficient, exact solution methods for these models. In addition, we introduce a power reliability-oriented risk measure and present new, computationally efficient models for risk-averse grid planning and operations.

math.OC↗

arXiv2025

Baseline hydropower generation offer curves

We outline a mathematical model for pricing hydropower generation. The model involves a Markov decision process that reflects the seasonal variation in historical time series of water inflows. The procedure is computationally efficient and easy to interpret.

math.OC↗

arXiv2025

On monotone completion of risk markets: Limit results for incomplete risk markets

We consider a competitive market with risk-averse participants. We assume that agents' risks are measured by coherent risk measures introduced by Artzner et al. (1999). Fundamental theorems of welfare economics have long established the equivalence of competitive equilibria and system welfare optimization (see, e.g., Samuelson (1947)). These have been extended to the case of risk-averse agents with complete risk markets in Ralph and Smeers (2015). In this paper, we consider risk trading in incomplete markets and introduce a mechanism to complete the market iteratively while monotonically enhancing welfare.

math.OC↗

arXiv2024

Quantile Fourier regressions for decision making under uncertainty

Weconsider Markov decision processes arising from a Markov model of an underlying natural phenomenon. Such phenomena are usually periodic (e.g. annual) in time, and so the Markov processes modelling them must be time-inhomogeneous, with cyclostationary rather than stationary behaviour. We describe a technique for constructing such processes that allows for periodic variations both in the values taken by the process and in the serial dependence structure. We include two illustrative numerical examples: a hydropower scheduling problem and a model of offshore wind power integration.

math.OC↗

arXiv2022

Asymptotic welfare performance of Boston assignment algorithms

We make a detailed analysis of three key algorithms (Serial Dictatorship and the naive and adaptive variants of the Boston algorithm) for the housing allocation problem, under the assumption that agent preferences are chosen iid uniformly from linear orders on the items. We compute limiting distributions (with respect to some common utility functions) as $n\to \infty$ of both the utilitarian welfare and the order bias. To do this, we compute limiting distributions of the outcomes for an arbitrary agent whose initial relative position in the tiebreak order is $θ\in[0,1]$, as a function of $θ$. The results for the Boston algorithms are all new, and we expect that these fundamental results on the stochastic processes underlying these algorithms will have wider applicability in future. Overall our results show that the differences in utilitarian welfare performance of the three algorithms are fairly small but still important. However, the differences in order bias are much greater. Also, Naive Boston beats Adaptive Boston, which beats Serial Dictatorship, on both utilitarian welfare and order bias.

econ.TH↗

arXiv2017

Multi-district preference modelling

Generating realistic artificial preference distributions is an important part of any simulation analysis of electoral systems. While this has been discussed in some detail in the context of a single electoral district, many electoral systems of interest are based on multiple districts. Neither treating preferences between districts as independent nor ignoring the district structure yields satisfactory results. We present a model based on an extension of the classic Eggenberger-Pólya urn, in which each district is represented by an urn and there is correlation between urns. We show in detail that this procedure has a small number of tunable parameters, is computationally efficient, and produces "realistic-looking" distributions. We intend to use it in further studies of electoral systems.

cs.GT↗

arXiv2012

Power measures derived from the sequential query process

We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual power in simple games, and show that, as for the Shapley-Shubik index, they extend naturally to measures for TU-games. In particular, the individual measures include all weighted semivalues. We single out the simplest measure in our family for more investigation, as it is new to the literature as far as we know. Although it is very different from the Shapley value, it is closely related in several ways, and is the natural analogue of the Shapley value under a nonstandard, but natural, definition of simple game. We illustrate this new measure by calculating its values on some standard examples.

math.CO↗

arXiv2012

Probability calculations under the IAC hypothesis

We show how powerful algorithms recently developed for counting lattice points and computing volumes of convex polyhedra can be used to compute probabilities of a wide variety of events of interest in social choice theory. Several illustrative examples are given.

math.CO↗

arXiv2007

Asymptotics of the minimum manipulating coalition size for positional voting rules under IC behaviour

We consider the problem of manipulation of elections using positional voting rules under Impartial Culture voter behaviour. We consider both the logical possibility of coalitional manipulation, and the number of voters that must be recruited to form a manipulating coalition. It is shown that the manipulation problem may be well approximated by a very simple linear program in two variables. This permits a comparative analysis of the asymptotic (large-population) manipulability of the various rules. It is seen that the manipulation resistance of positional rules with 5 or 6 (or more) candidates is quite different from the more commonly analyzed 3- and 4-candidate cases.

math.PR↗