[求助]看不懂这句话的意思

In OG11 RC

In 1955 Maurice Duverger published The Political Role of Women, the first behavioralist, multinational comparison of women's electoral participation ever to use election data and survey

(5)      data together. His study analyzed women's patterns of voting, political candidacy, and political activism in four European countries during the first half of the twentieth century. Duverger's research findings were that women voted somewhat less frequently

(10) than men (the difference narrowing the longer women had the vote) and were slightly more conservative.

看不懂这句话的意思"the difference narrowing the longer women had the vote",语法上好像也不通啊，怎么理解呢。请大侠指点迷津。