Estimation of the voter transition matrix

Assessing uncertainty of voter transitions estimated from aggregated data. Application to the 2017 French presidential election

“…A different way followed by other authors is to approach the subject as a mathematical programming problem, looking for the values 𝑝 𝑗𝑘 of the vote transition matrix that, fulfilling certain restrictions, minimize, in some sense, the discrepancy with the outcomes recorded in the different territorial units. McCarthy and Ryan (1977) propose a quadratic program model to minimize the sum of squares of these discrepancies, Tziafetas (1986) suggests minimizing the sum of their absolute values, which transforms the model into a linear program, and Corominas et al (2015) explore four possible optimality criteria to estimate the 𝑝 𝑗𝑘 . Although the mathematical programming approaches share some similarities with the ecological regression methods when the sum of squares of the discrepancies is used as loss function, these have the advantage of not requiring assuming any particular probability distribution to guarantee that the 𝑝 𝑗𝑘 estimates are logically consistent.…”

“…According to this definition, the 𝑝 𝑗𝑘 proportions must inevitably fulfil constraints (1), ( 2) and (3). The mathematical programming models proposed in McCarthy and Ryan (1977) and Tziafetas (1986) include constraints (1) and (3). Constraints (2) are similar to those proposed in Johnston and Hay (1983), Romero (2014) and Corominas et al (2015).…”

“…This second innovation is the main contribution of our paper. No other previously published method based on linear or quadratic programming (e.g., McCarthy and Ryan, 1977;Tziafetas, 1986;Vázquez and Romero, 2001;Romero, 2014;Corominas et al, 2015) measures this issue. Uncertainty is routinely estimated in ecological regression approaches.…”

Computing voter transitions: The elections for the Catalan Parliament, from 2010 to 2012

“…Tziafetas (1986) uses an approach similar to that of McCarthy and Ryan (1977) and a variant of it, which consists in using the absolute value of the deviations instead of the squares of them. Upton (1978), concerning McCarthy and Ryan's approach, observes that it gives a high proportion of zeroes in the matrix and concludes that overestimates the proportion of stayers (voters that do not change their preferences between the to elections -actually, electors that vote for options whose name is the same in both elections−, contrasting with movers).…”

Análisis de la incertidumbre en la estimación de la movilidad electoral mediante el procedimiento LPHOM

“…McCarthy y Ryan (1977) proponen al respecto un modelo de programación cuadrática para minimizar las discrepancias entre los resultados obtenidos por el modelo y los constatados en cada una de las I unidades territoriales para cada una de las K opciones. Tziafetas (1986) sugiere minimizar la suma de los valores absolutos de estas discrepancias, lo que transforma el modelo en un Programa Lineal más fácil de resolver, enfoque similar al propuesto por Vázquez y Romero (2001) que plantean diferentes alternativas para la función a optimizar, como hacen también Corominas, Lusa y Valvet (2015). Romero (2014) plantea en su modelo una alternativa novedosa para abordar el problema de los cambios en el censo entre los dos procesos electorales.…”