Background: In some countries every citizen has the right to obtain a designated general practitioner. However, each individual may have preferences that cannot be fulfilled due to shortages of some kind. The questions raised in this paper are: To what extent can we expect that preferences are fulfilled when the patients "compete" for entry on the lists of practitioners? What changes can we expect under changing conditions? A particular issue explored in the paper is when the majority of women prefer a female doctor and there is a shortage of female doctors.
Findings: The analysis is done on the macro level by the so called gravity model and on the micro level by recent theories of benefit efficient population behaviour, partly developed by two of the authors. A major finding is that the number of patients wanting a doctor of the underrepresented gender is less important than the strength of their preferences as determining factor for the benefit efficient allocation.
Conclusions: We were able to generate valuable insights to the questions asked and to the dynamics of benefit efficient allocations. The approach is quite general and can be applied in a variety of contexts.