From the Archives: Condorcet, Brigham, and Succession to the Presidency

August 19, 2006 | 8 comments
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Condorcet was a French social theorist in the opening decades of the 19th century and is credited with first discovering a paradox of majority voting that bears his name. Here is the paradox: Imagine that you have a group of three people (A,B, and C) who are voting on three different alternatives (X, Y, and Z). A prefers X to Y and Y to Z. B prefers Y to Z and Z to X. C prefers Z to X and X to Y. If X is paired in a vote with Y, then X wins (A and C against B). If Y is paired with Z, then Y wins (A and B against C). But — and this is the kicker — if Z is paired with X, then Z wins (B and C against A). In other words, even if the individual preferences of A, B and C are transitive, the collective preferences of A, B, and C are not. Put in starker terms, if you control the order the votes are taken in, then you can get any outcome you want because any choice can be defeated by one of the others. I have often wondered if this paradox might in part account for how Brigham Young became president of the Church.

When Joseph was murdered, it was not clear to the Saints who his successor should be. There were lots of claimants, but in the months immediately after his death the biggies were Sydney Rigdon and the Quorum of the Twelve. In August of 1844 a conference was held. Both Brigham and Sydney spoke, and then Sydney put to the conference the question of whether they would prefer to be led by himself of the Quorum of the Twelve. The conference voted in favor of the Twelve and Sydney left Nauvoo to found his own church, which rapidly fell to pieces. More than three years later, a conference in Winter Quarter’s voted to make Brigham Young President of the Church.

Notice the way the votes were ultimately paired. First it was the Twelve versus Rigdon and the Twelve won. Then it was the Twelve versus Brigham and Brigham won. Condercet teaches us, however, that the mere fact that Brigham beat the alternative that beat Sydney does not necessarily mean that Brigham could have beat Sydney. In other words, the outcome might have been different had the votes been taken in a different order.

Of course, this need not necessarily have been the case. Brigham might have beaten Sydney if the vote had been put that way in 1844. I don’t think that we really know enough about the preferences of the voters to ever be certain one way or the other. Very few people voted in favor of Sydney at the 1844 conference and he probably would have lost regardless of how the votes were structured. Who knows! Still, it is an intriguing little possibility.

Democratic theorists have often been troubled by Condercet’s Paradox, and by its more rigorous theorization by Kenneth Arrow. It seems to suggest that at least under some circumstances, majority will is a fiction. There is simply the order in which the votes are taken. (Or in the absence of such agenda setting, endless cycling of alternatives.) However, if majority will is a fiction we are simply being ruled by the agenda setters.

Interestingly, there is one way of insuring that you never run into the problem of Condercet’s Paradox. In place of a majority wins rule, you substitute a super-majority or unanimity requirement. Interestingly, if what we are told is correct, the Quorum of the Twelve has adopted such a unanimity requirement. No action is taken unless everyone agrees. Obviously, this would create its own interesting dynamics, but it does insure that institutional decisions are not simply the random result of the order in which the votes are taken.

8 Responses to From the Archives: Condorcet, Brigham, and Succession to the Presidency

  1. It's Not Me on August 19, 2006 at 10:50 pm

    I know this is very crude, but this reminds me of sports. While the outcome of a contest is decided by a tally of the final points, the journy to that finaly tally is not always decided by the strongest or the best, but occasionally by the order of the occurrence of certain circumstances.

  2. It's Not Me on August 19, 2006 at 10:52 pm

    I’m not sure that came out right, but with much thought and prayer I think you can discern what I mean.

  3. Wacky Hermit on August 19, 2006 at 10:59 pm

    It’s nice to see that there’s someone else out there who thinks about voting theory. :)

  4. Hans on August 19, 2006 at 11:18 pm

    One of the reasons Sidney (with an “i”, not a “y”!) Rigdon put forth a claim to lead the church was by reason that, as far as he was concerned, a.) he was still the First Counselor in the First Presidency, and b.) he believed that after Joseph Smith was killed, there would be no other prophet, thus he offered himself as a Guardian of the Church. He was excommunicated for apostasy on Sept. 8, 1844 and never returned to the church.

    http://personal.bellsouth.net/w/o/wol3/rigdos1.htm

  5. Bill on August 19, 2006 at 11:22 pm

    Condorcet, please

  6. Kaimi Wenger on August 20, 2006 at 12:06 am

    Prior comments on this post available at http://www.timesandseasons.org/?p=247

  7. Mark Ashurst-McGee on August 21, 2006 at 12:12 pm

    I don’t see how unanimity changes the main issue if the entire group isn’t setting the agenda (formulating the prosposals to vote on and the sequence of proposals).

  8. YL on August 22, 2006 at 2:16 pm

    Joseph Smith, under the Lord’s direction, set up the procedure of succession: D & C 107 says that, when there is no 1st presidency, the Quorum of the Twelve presides over the Church with authority equal to that of the First Presidency. Joseph Smith’s case is different ONLY because he had to be the one to establish the Quorum of the Twelve, and thus couldn’t be called by them. Because of D & C 107, there should have been NO confusion as to who presided over the Church after Joseph’s death. There certainly was NO confusion in Brigham Young’s mind because previously Joseph had taught the members of the Twelve about their powers. But as usual the Saints had NOT read the scriptures and so were confused.

    So when Joseph Smith died, the First Presidency was automatically dissolved. Technically speaking, when the president of any quourm is released (or when a bishop or stake president or relief society president is released), his or her counselors are automatically released because they were called specifically to be counselors to that particular president or bishop. That’s why when a new president or bishop or relief society president is called, and if he or she has the same counselors as the previous bishop or president or relief society president, then the counselors are released along with the previous bishop or president or relief society president, and are sustained as counselors to the new bishop or president or relief society president.

    Therefore, when Joseph Smith died, his counselors were automatically released. That’s why Sidney Rigdon was UNrighteous when he said he should preside over the Church; Sidney, after all, was Joseph Smith’s spokesman. Understanding D & C 107 and the authority of the Quorum of the Twelve, Brigham Young responded to Sidney Ridgon: “Well, then go where Joseph is and be his spokesman.” With no first presidency the Quorum of the Twelve presided over the church with authority equal to that of the First Presidency, according to D & C 107.

    Also, because the Quorum of the Twelve has authority equal to that of the First Presidency [when there's no First Presidency], the Quorum has the authority to establish the First Presidency – just as God’s messengers had the right to establish Joseph as the prophet.

    D & C 107 also says that when the First Presidency exists, then the Quorum of the Twelve serves under the First Presidency.

    When the Quorum of the Twelve is presiding over the Church, the President of the Quorum of the Twelves is THE PROPHET, SEER, & REVELATOR – just as the President of the First Presidency is THE PROPHET, SEER, & REVELATOR.

    Thus, some Latter-Day Saints have WRONGLY said that there have been periods in Church history when we’ve been without a prophet. There have been periods where we’ve been without a First Presidency. But since the establishment of the Church in 1830, the Church has NEVER been without a prophet for even a single second because: the very instant the prophet dies, the Quorum of the Twelves is presiding over the Church, and the President of the Twelve is THE PROPHET, SEER, AND REVELATOR – until the First Presidency is reorganized.

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