Continuous clustered proportion data often arise in various areas of the social and political sciences where the response variable of interest is a proportion (or percentage). An example is the behavior of the proportion of voters favorable to a political party in municipalities (or cities) of a country over time. This behavior can be different depending on the region of the country, giving rise to groups (or clusters) with similar profiles. For this kind of data, we propose a finite mixture of a random effects regression model based on the L-Logistic distribution. A Markov chain Monte Carlo algorithm is tailored to obtain posterior distributions of the unknown quantities of interest through a Bayesian approach. To illustrate the proposed method, with emphasis on analysis of clusters, we analyze the proportion of votes for a political party in presidential elections in different municipalities observed over time, and then identify groups according to electoral behavior at different levels of favorable votes.