Only recently has the AAAS disclosed the election process to the Academy on its website. An excerpt (I've bolded some bits):
- Preliminary Evaluation Ballot – The first round of voting is the Preliminary Evaluation Ballot (PEB), which includes the names of all eligible nominees in a given section and is distributed to all voting members of that section. Section panels, comprised of usually 5-10 members, review the PEB results and select approximately 12 candidates (not including candidates for International Honorary Membership) in their sections to advance to the next round.
- Appraisal List – The second-round ballot, usually consisting of 350-400 names, is distributed to all voting members in the winter. Once again, on the basis of the ballot results, the Academy’s five class committees recommend approximately 6 candidates in each section for election plus suggestions for International Honorary Members.
- Election - The Academy’s Council and Board of Directors are responsible for reviewing and approving the slate of candidates recommended for election. Results are announced in mid-April.
The primary criteria for election are excellence in the field and a record of continued accomplishment. The section panels and class committees are also responsible for recommending a representative and diverse slate of candidates in terms of gender, race, ethnicity, institutions, geography, disciplines and balance of fields that includes both practitioners and scholars.
This suggests what I have been told in the past, namely, that the selection panels for each section have a real impact on the final results, and are not strictly bound by the vote of the membership. That means, of course, that the composition of the section panel is quite important. (Also notable here is the mention of institutional diversity: last year, the University of Chicago had 15 faculty elected, this year just 4. It appears they are taking this more seriously than in the past.)