For the first time since 1977, the
The blogosphere is filled with similar consternation and disbelief that each submission seemingly failed to satisfy the Pulitzer Board's standard of excellence. The board's web page appears to lend support to this view, stating: "If in any year all the competitors in any category shall fall below the standard of excellence fixed by The Pulitzer Prize Board, the amount of such prize or prizes may be withheld."
While the board has not disclosed its manner of selection, we do know that a majority opposed each finalist. Rather than demonstrating a lack of excellence, however, the impasse more likely resulted from a phenomenon known as cycling. Cycling can arise when three or more decision-makers select among at least three options, as was the case with the 20-member board's selection among three finalists.
Imagine that the board split into three factions: Group 1, which found most appealing "Swamplandia!'s" dysfunctional family challenged in and out of a theme park amid alligator-infested waters; Group 2, which was most intrigued by "The Pale King," the cobbling together a suicidal author's unfinished novel raising existential questions about tedium in a Reagan-era IRS office; and Group 3, which loved the novella "Train Dreams" and the mystical adventures of a Prohibition-era day laborer in the Idaho Panhandle transformed by great personal tragedy amid a rapidly changing American landscape.
Assume that no single group, but that any two groups, form a majority. Because no single group prevails, the groups rank their preferences over all three works. Group 1 ranks the works "Swamplandia!," then "The Pale King," then "Train Dreams"; Group 2 ranks them "The Pale King," then "Train Dreams," then "Swamplandia!"; and Group 3 ranks them "Train Dreams," then "Swamplandia!," then "The Pale King." With no majority winner, the board takes separate votes over paired comparisons until a winner prevails. If each group votes honestly, Groups 1 and 3 select "Swamplandia!" over "The Pale King," and Groups 1 and 2 select "The Pale King" over "Train Dreams." For an individual, the resulting ranking ("Swamplandia!," "The Pale King," "Train Dreams") would imply that "Swamplandia!" prevails against "Train Dreams." Despite this, and completing the cycle, Groups 2 and 3 choose "Train Dreams" over "Swamplandia!"
In the absence of a majority winner, group preferences do not necessarily "cycle" in this way. Consider changing Group 3's preferences to "Train Dreams," "The Pale King," "Swamplandia!" With this reversal of the Group 3's second and third listed rankings, the same pairwise voting protocol reveals that Groups 2 and 3 prefer "The Pale King" to "Swamplandia!" and that Groups 1 and 2 prefer "The Pale King" to "Train Dreams." In this case, "The Pale King," even though it is not a first choice majority winner, defeats all others in direct contests, a result known as a Condorcet winner.
The preceding voting protocol and others like it ensure that Condorcet winners prevail when they exist, but risk cycling when there is no Condorcet winner. When a majority of voters opposes each option, most likely the voting rule shares the feature of guaranteeing a Condorcet winner, but there is no Condorcet winner among the available entries.
There are alternative voting regimes that ensure winners despite cycling, but they introduce other difficulties. A rule permitting only two votes over three options empowers whoever sets the agenda to favor his or her preferred choice, or, conversely, the rule encourages participants to avoid such results by voting strategically. Still other voting practices encourage various forms of compromise or log rolls.
There is no perfect voting protocol. Any regime risks occasional frustration. For these brilliant authors and their families, it is small consolation that not winning more likely resulted from the voting procedures than from any negative assessment of quality. But for the rest of us, it is helpful to know that groups can fail to choose a winner without choosing to fail all entries.