Some potential questions for consideration, please suggest more ideas:
Which elected councillors are most at risk?
Which councillors both over and under performed, given the characteristics of the local area?
Which factors are correlated with votes for/against the incumbent party? (thanks @ktloh)
How have certain localities changed in voting patterns over the years? (thanks @ktloh)
Have new elections - directly elected mayors, combined authorities, police commissioners - increased voter turnout and if so, has this persisted over time?
What factors lead to the rise and fall of right wing parties?
Whilst turnout is generally higher in rural areas, is there a critical size beyond which turnout declines?
Some potential questions for consideration, please suggest more ideas: