Add mechanism for increasing board size

board.md

@@ -219,7 +219,7 @@ There are several goals of the design of this process:
 * Avoidance of too-frequent calls for applications
 * Accommodation for a scenario when more or fewer excellent candidates apply
   than the number of leaving Board members
-* A desire to keep the size of the Board at no more than 14 members
+* A desire to keep the size of the Board at roughly 14 members
 
 While the sections below spell out the rules, we give a brief overview here.
 Every year, we put out a call for
@@ -255,8 +255,7 @@ is already 14, then we have no more room and will not run an application
 process.
 
 The result of the application process is an appointment of zero or more
-directors, such that the total number of members stays below or
-equal to 14.
+directors.
 
 When an application process is triggered, the Secretary orchestrates the
 application process, below.
@@ -308,17 +307,24 @@ to email the Secretary directly and thus keep their preferences more private.
 Because the votes can contain explanations, some Board members may choose to
 update their votes. This is allowed up until April 1; only the final vote counts.
 
+The final votes are processed by the Shulze algorithm to produce a ranking
+of candidates, including the special candidate "That's it". All candidates listed
+above or tied with "That's it" would normally be invited to join the board.
+If the resulting board size would be more than 14, we must take a *board size
+exception vote*,
+described in the next subsection:
+we wish the board to remain agile enough to hold group conversations, and yet
+also want the flexibility to accept a large crop of excellent volunteers.
+
 Once candidates are selected, they are contacted by the Chair in rank
 order and invited to
 join the Board, with the Chair working down the list if anyone declines.
 The Chair stops this process if either:
-* the Board reaches size 14
+* the Board reaches size determined by board size exception vote
 * the Chair reaches "That's it" in the ranking
 If either of these conditions happens in the midst of a tie in the ranking,
-the Chair stops sending invitations. (That is, if there are 13 members of the
-Board and the next two candidates are tied, neither is invited. Similarly,
-if the next candidate is tied with "That's it" in the ranking, they are not
-invited.)
+the Chair sends invitations to all final tied candidated. (That is, if there are 13 members of the
+Board and the next two candidates are tied, both are invited.)
 
 For example, suppose Soomin Kim, Chris Young, and Jens Pedersen are applying.
 One ranking might be
@@ -335,11 +341,67 @@ This voting system has been used for several years by the GHC Steering
 Committee. While somewhat complex to describe, it is easy to understand and
 use as a voter and works well in practice.
 
-If the number of members voted in by this procedure would cause the total size
-of the board to exceed its maximum from the last 12 months, then the decision
-must be ratified by a 2/3 majority of the board.
-
-## 7.6. Selection Criteria
+## 7.6. Board Size Exception
+
+These rules suggest that the board size is capped at 14. However, an exceptional
+crop of candidates may come along, encouraging us to increase our size. This
+section lays out the rules for this scenario.
+
+Before exercising these rules, a standard board candidate vote is taken, with
+all non-rerunning board members voting their slate of candidates (including "That's it").
+These votes are tabulated to produce the final candidate ranking.
+
+At this point, the final ranking is shared with the entire board,
+including rerunning members. Then all board members (including
+rerunning members) submit a vote comprising their desired board size
+(just one number, which must be at least 14), in light of the current
+board membership and the new members being voted in.
+
+Let *twoThirdsSupport* be a function from a list of integers to
+an integer; it evaluates to the greatest integer *n* such that at least
+two thirds of *votes* are greater than or equal to *n*. Example:
+*twoThirdsSupport*([16, 14, 19, 18, 18, 15, 14]) is 15: there are 5 votes
+greater than or equal to 15, 5 is greater than or equal to 2/3 of 7
+(the length of the list), and 15 is the greatest such number (16 is supported
+by only 4 votes, which is not enough).
+
+Let *m* = *twoThirdsSupport*(non-rerunning members' votes)
+and *n* = *twoThirdsSupport*(all board members' votes). Then the desired
+board size is *min*(*m*, *n*). This board size is used to determine when
+the invitation process for new members stops.
+
+Note that this process must be repeated every year in which the "That's it"
+voting process would lead to a board size over 14; increasing size one year
+does not imply it for any future year.
+
+**Rationale.** We don't want to, say, individually vote on all candidates
+that appear above 14 -- that would lead to acrimony and take much time. Instead,
+the concern is just about numbers here (in light of the actual candidates selected,
+which is fixed).
+
+It is tempting to just have the non-rerunning board members
+vote, but this has a failure mode: if, say, one year has a particularly large crop
+of rerunning members, the non-rerunning members could, say, invite 100 of their
+friends and minority of the entire board could take over the operation of the HF.
+Thus increasing the board size should be done carefully. By having rerunning board
+members vote here, the size increase can happen only by agreement of 2/3 of the
+entire board.
+
+One might worry about conflict of interest. After all, this process allows
+rerunning members to effectively vote on their own destiny. However, the fact
+that the ranking of candidates has been fixed (and shared) beforehand eliminates
+the conflict:
+
+* For a member ranked toward the beginning of the list (such that they would be
+selected before the size reaches 14), there is no conflict: this person is going
+to remain on the board regardless of their vote.
+
+* For a member ranked toward the end of the list, they can be included in the new
+board only if 2/3 of the non-rerunning members also wish to include them. Their
+vote can matter only if it excludes themselves, also effectively avoiding the
+conflict.
+
+## 7.7. Selection Criteria
 
 While we do not expect all applicants to meet all criteria, here are the
 qualities we seek in an application:
@@ -383,7 +445,7 @@ Simultaneously hitting all these criteria is nigh impossible. However, each
 subsequent round of applications for new Board members offers a fresh chance
 to rectify any imbalances.
 
-## 7.7. Balancing Terms
+## 7.8. Balancing Terms
 
 Ideally, roughly a third of the Board would expire every year.
 After the initial appointment of Board members and occasionally thereafter
@@ -785,4 +847,4 @@ This section describes typical attributes for votes.
     1. Any two Board members may change an MR vote to another form of vote (likely: an operational
        vote or a two-third vote) simply by requesting to do so. In this way, if the automatic abstention
        mechanism appears harmful (because the contents of an MR look contentious, say), it can be
-       circumvented.
\ No newline at end of file
+       circumvented.