Supermajority = Will of God?
I note fellow practical libertarian blog Marginal Revolution, by Alex Tabarrock, brought to my attention the Papal Election and that it was apparently the Catholic Church that originated the concept of Supermajority Voting, in which a 2/3 majority is required to elect a pope up until the 31st ballot. This is commented on by jewish blog "yesh omrim" which brings in commentary from a theologian at Boston College who speaks on this and the issue of infallibility of the pope versus the fact he is elected by a fallible group of electors.
The writer of yesh omrim and his wife ask if the Pope gets his infallibility by being elected, or whether the electors gain it by being in conclave. While John Paul II's Universi Dominici Gregis seems to favor the first option....
"Alex Tabarrok quotes Pope Pius II as saying “What is done by two thirds of the sacred college, that is surely of the Holy Ghost, which may not be resisted.” That sounds a lot like the second option. (But my wife wants to know what spirit is supposed to be resting on the cardinals who voted against the winning candidate, especially since under Universi Dominici Gregis, a Pope can be elected by a simple majority on the thirty-first ballot.) "
It turns out that my dear cousin, Haidee Lorrey, has something to say about this [Prior linked article disabled, final draft is now going to press]. Haidee is an Oxford educated medeivalist, so while I've never checked to see if she knows her stuff, as if I could tell, I will presume that given she got her degree and has written six books in her field, that she does know what she is talking about. While the draft I've linked to specifically says that it is not to be referenced without prior permission, as it is a work in progress, I shall assume that this means referenced in academically refereed papers, and since a number of others have already breached the ramparts, at least in the blogosphere, I shall not be guilty of burgling dear cousins barn after the horses have already been stolen by others.
There are a number of interesting discoveries in this paper, which examines the work of Ramon Lull (ca 1232--1316), an arab educated native of Palma who was a polymathic talent in poetry and fiction, mathematics and logic, who felt called by God to write a book on his concepts of "Ars Generalis", which, among other things, included a commentary on the art of voting. His disciple, Nicolaus Cusanus (ca 1401---1464) were early thinkers on democracy in the medeival period who developed their theories in ignorance of the advances of Greek and Latin political scientists of the previous age. Lull devised voting techniques which anticipate Copeland and Borda, as well as Condorcet, it turns out.
In this, Haidee (who I shall hereafter refer to as H. Lorrey, though she isn't the only H. Lorrey in our family) and her co-author, Iain McLean of Nuffield College, Oxford, seem to rehabilitate Null when they say,
It was then to his disciple, Cusanus, who attended the Council of Basel in 1431, which "aggressively asserted its superiority to the pope (Sigmund 1991, xiv)", who developed his masterpiece of political theory, "De concordantia catholica" to prescribe his opinion of best practices for electing a Pope, as well as the Holy Roman Emperor. Rather than lean toward Condorcet, as Lull had done, Cusanus seems to have preferred Borda schemes with secret voting apparently because he believed that voters would weigh some issues or characteristics as more important than others, which the method preferred by Lull did not allow for.
Unanimity was the original rule to "reveal God's will", but was the source of many conflicts and schisms. This was the source of the many Pope/Anti-Pope schisms of the dark ages back to the Roman era, according to H. Lorrey, in which two or more Popes would be simultaneously elected after months of hung conclaves.
The Church replaced it with the 2/3 supermajority in 1179 and included what was then an innovative form of approval balloting in conclave from the 13th century onwards to the 17th, but tended toward coalition-building phenomena which both Lull and Cusanus had developed their theories to help combat. Previously, in 1059, the papal bull of Pope Nicholas II had excluded the lay people from participating in the elective process, which they had previously enjoyed. The Emperor of the Holy Roman Empire himself could only accept the Church's decision. Excluding the lay people did not eliminate the anti-pope phenomenon, so it was decided to move to a 2/3 supermajority system.
It was not until 1988 and 1991 that Caplin and Nalebuff demonstrated mathematically the superiority of the 2/3 supermajority rule:
As this rule only applies in n candidate election-spaces. Note the specification that two candidate races require a 55% majority for a stable result. This is as good an explaination as any as to why US presidential politics have been so contentious since the end of the Reagan era. Where Reagan was able to compile solid victories, no candidate since has gained that large a percentage of the popular vote, and as a result have had controversial Presidencies fraught with popular conspiracy theories, vicious partisanship, polarizing debate semantics, and historically high distrust in government and elected officials.
It may also explain why the US electoral system has tended toward a two party system and simultaneously remained the most stable democracy in history, while most other democratic nations which tend toward consensus building and factionalism have established terrible records toward instability and electoral schizms, such as the elections of Hitler, Hussein, and Mussolini.
If the Libertarian Party were to gain greater popular traction, we should expect to see greater political conflict in the entire populace, and a need for higher majority needed for winning parties to declare a mandate and establish popular stability. However, doing so would increase the risk of dictatorship as a scared populace, unused to thinking for themselves for a change and having to make complex choices between three or more candidates, would tend to attract toward demagogues, charlatans, and Big Brother types intent on trading liberty for security. We might expect that the present Bush regime is the result of the factional instabilities of the 1990's, brought on by Perot's Reform Party and the popular disgust with entrenched incumbents in Congress that that movement fed off of, and not just popular fear of foreign terrorism against America.
This is a tendency we will need to be aware of, and I think is a big reason why the Party needs to coalition build with one of the main parties if it is to both succeed electorally as well as in implementing its goals of greater liberty, rather than being a root cause or excuse for the implementation of fascism.
The writer of yesh omrim and his wife ask if the Pope gets his infallibility by being elected, or whether the electors gain it by being in conclave. While John Paul II's Universi Dominici Gregis seems to favor the first option....
"Alex Tabarrok quotes Pope Pius II as saying “What is done by two thirds of the sacred college, that is surely of the Holy Ghost, which may not be resisted.” That sounds a lot like the second option. (But my wife wants to know what spirit is supposed to be resting on the cardinals who voted against the winning candidate, especially since under Universi Dominici Gregis, a Pope can be elected by a simple majority on the thirty-first ballot.) "
It turns out that my dear cousin, Haidee Lorrey, has something to say about this [Prior linked article disabled, final draft is now going to press]. Haidee is an Oxford educated medeivalist, so while I've never checked to see if she knows her stuff, as if I could tell, I will presume that given she got her degree and has written six books in her field, that she does know what she is talking about. While the draft I've linked to specifically says that it is not to be referenced without prior permission, as it is a work in progress, I shall assume that this means referenced in academically refereed papers, and since a number of others have already breached the ramparts, at least in the blogosphere, I shall not be guilty of burgling dear cousins barn after the horses have already been stolen by others.
There are a number of interesting discoveries in this paper, which examines the work of Ramon Lull (ca 1232--1316), an arab educated native of Palma who was a polymathic talent in poetry and fiction, mathematics and logic, who felt called by God to write a book on his concepts of "Ars Generalis", which, among other things, included a commentary on the art of voting. His disciple, Nicolaus Cusanus (ca 1401---1464) were early thinkers on democracy in the medeival period who developed their theories in ignorance of the advances of Greek and Latin political scientists of the previous age. Lull devised voting techniques which anticipate Copeland and Borda, as well as Condorcet, it turns out.
In this, Haidee (who I shall hereafter refer to as H. Lorrey, though she isn't the only H. Lorrey in our family) and her co-author, Iain McLean of Nuffield College, Oxford, seem to rehabilitate Null when they say,
These works show that Lull does not deserve the scornful treatment he gets in modern histories of mathematics and logic. He was obsessed with comparisons of objects in pairs. The properties of the formula for the combination of two objects from a larger n, which he was probably one of the first mathematicians in the West to import from the Arab world, fascinated him endlessly and fueled the magnificent but impossible dream of the General Art. Lull believed that applying successive pairwise combinations of virtues could lead one to "demonstrating the truth of the holy Catholic faith through the use of necessary reasons to those who are ignorant of it" (Bonner 1985, 69). This is what led Donald Michie, the eminent computer scientist, to label Lull "one of the most inspired madmen who ever lived" (Gardner 1982, ix). Martin Gardner has written that Lull's life was "much more fascinating than his eccentric logic. . . . Lull's mistake . . . was to suppose that his combinatorial method had useful applications to subject matters where today we see clearly that it does not apply" (Gardner 1982, xiv, 18). However, the application to voting rules is perhaps Lull's most fruitful use of the principle of pairwise combination. Unlike others it is an entirely appropriate application of the mathematics of combinations, not repeated until 1785.
It was then to his disciple, Cusanus, who attended the Council of Basel in 1431, which "aggressively asserted its superiority to the pope (Sigmund 1991, xiv)", who developed his masterpiece of political theory, "De concordantia catholica" to prescribe his opinion of best practices for electing a Pope, as well as the Holy Roman Emperor. Rather than lean toward Condorcet, as Lull had done, Cusanus seems to have preferred Borda schemes with secret voting apparently because he believed that voters would weigh some issues or characteristics as more important than others, which the method preferred by Lull did not allow for.
Unanimity was the original rule to "reveal God's will", but was the source of many conflicts and schisms. This was the source of the many Pope/Anti-Pope schisms of the dark ages back to the Roman era, according to H. Lorrey, in which two or more Popes would be simultaneously elected after months of hung conclaves.
The Church replaced it with the 2/3 supermajority in 1179 and included what was then an innovative form of approval balloting in conclave from the 13th century onwards to the 17th, but tended toward coalition-building phenomena which both Lull and Cusanus had developed their theories to help combat. Previously, in 1059, the papal bull of Pope Nicholas II had excluded the lay people from participating in the elective process, which they had previously enjoyed. The Emperor of the Holy Roman Empire himself could only accept the Church's decision. Excluding the lay people did not eliminate the anti-pope phenomenon, so it was decided to move to a 2/3 supermajority system.
It was not until 1988 and 1991 that Caplin and Nalebuff demonstrated mathematically the superiority of the 2/3 supermajority rule:
"when more voters prefer intermediate candidates than the average of those favoring extremes, there exists an unbeatable proposal, and furthermore no cycles are possible. In general, the majority rule needed to avoid cycles and ensure existence of an unbeatable proposal in a n-dimensional issue space is no higher than 1- [n/(n+1)]n. This rule is thus equal to 55% for two dimensional spaces, to 57% for three-dimensional spaces, and, being increasing in n, its limit is just under 64%. In a different and apparently unrelated approach, it has also been asserted that for three candidates "it is impossible to have a cycle where each candidate beats another candidate by receiving more than two-thirds of the vote”. The general rule which makes cycles impossible is equal to (n1)/n, n being in this case the number of candidates (Saari, 1994: 92-93; 1995: 62). This means that the 2/3 rule used to elect the Pope produces a stable outcome with up to three candidates, a number which could be expected from a college of voters with three orders"
As this rule only applies in n candidate election-spaces. Note the specification that two candidate races require a 55% majority for a stable result. This is as good an explaination as any as to why US presidential politics have been so contentious since the end of the Reagan era. Where Reagan was able to compile solid victories, no candidate since has gained that large a percentage of the popular vote, and as a result have had controversial Presidencies fraught with popular conspiracy theories, vicious partisanship, polarizing debate semantics, and historically high distrust in government and elected officials.
It may also explain why the US electoral system has tended toward a two party system and simultaneously remained the most stable democracy in history, while most other democratic nations which tend toward consensus building and factionalism have established terrible records toward instability and electoral schizms, such as the elections of Hitler, Hussein, and Mussolini.
If the Libertarian Party were to gain greater popular traction, we should expect to see greater political conflict in the entire populace, and a need for higher majority needed for winning parties to declare a mandate and establish popular stability. However, doing so would increase the risk of dictatorship as a scared populace, unused to thinking for themselves for a change and having to make complex choices between three or more candidates, would tend to attract toward demagogues, charlatans, and Big Brother types intent on trading liberty for security. We might expect that the present Bush regime is the result of the factional instabilities of the 1990's, brought on by Perot's Reform Party and the popular disgust with entrenched incumbents in Congress that that movement fed off of, and not just popular fear of foreign terrorism against America.
This is a tendency we will need to be aware of, and I think is a big reason why the Party needs to coalition build with one of the main parties if it is to both succeed electorally as well as in implementing its goals of greater liberty, rather than being a root cause or excuse for the implementation of fascism.
posted by Mike Lorrey at 10:58 PM
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