Buchanan, On Majority Voting and Budgets, Thoughtful Thursday

James M. Buchanan and Gordon Tullock, The Calculus of Consent Ann Arbor Paperbooks, the University of Michigan Press, 1965.

A majority voting system can lead to wasteful expenditure. It does so because a majority can vote not to give the minority its fair share. A population has money to spend on education. It can even come from a higher government or from the petroleum that the country owns. Assume, there are three ethnic groups, A, B and C. Each are equal size and are as likely to exercise their franchise. A and B can vote together to spend all the money on educating their children and not appropriate any money for the schools that C uses. Assuming that the constitution or their morality did not prevent it, the coalition of A and B could vote that C pays all taxes and get none of the benefit. Of course, there is some question of the stability of a coalition, because the next year, Cand B could team up to shaft group A. In game theory terms, any of these voting patterns dominates A, B and C voting equal amounts of money to each group's schools. But nothing in game theory says which coalition will form and how long it will stay together.

But let us assume now that all three groups do have good schools and the question is whether to build a brand new school. As before, assume that groups A and B form a coalition to shaft C. They can spend ten million dollars on schools, but this will give only nine million dollars pleasure or utility total to A and B. And we will assume that A and B are not so crass as to simply take the cash out right from taxes and distribute as a cash grant to themselves. It is to their advantage to vote for the school buildings, since they get $4.5 million each of utility but only pay $3.33 million in taxes--part of their schools are paid by the hapless C. This is why one says that the democratic process leads to waste.

There is an apocryphal quote, A democracy cannot exist as a permanent form of government. It can only exist until the voters discover that they can vote themselves largess from the public treasury. From that moment on, the majority always votes for the candidates promising the most benefits from the public treasury with the result that democracy always collapses over loose fiscal policy." But as Loren Collins showed, it is not clear where this came from.

But representative democracy is even worse. Assume that there are fourty-nine people divided into seven districts. On a bill, their opposing and aye'ing is as follows.

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Four Aye, Three Naye

Four Aye, Three Naye

Four Aye, Three Naye

Four Aye, Three Naye

Seven Naye

Seven Naye

Seven Naye

Assume that we are fortunate enough to have representatives that alwaus vote what the majority of their districts want. Then, in Congress there will be four Aye's and three Naye's. This is even though of the population only sixteen aye's out of fourty-nine in favor. And it gets worse with larger populations, Dr. Buchanan and Turlock have an example of 39601 voters in 199 districts--only 10,000 voters would be noted to get an aye.

And the good doctors give an example of bicameral systems under total arrangement diversity. Here fourty-nine voters are arranged as follows:

S1	A	H	O	V	CC	II	PP
S2	B	I	P	W	DD	JJ	QQ
S3	C	J	Q	X	EE	KK	RR
S4	D	K	R	Y	FF	LL	SS
S5	E	L	S	Z	GG	MM	TT
S6	F	M	T	AA	HH	NN	UU
S7	G	N	U	BB	HH	OO	VV

Here sixteen of the voters can get a measure passed or defeated--again assuming that our representatives simply vote what the majority of their constituents want. But assume one of the red voters, Q defect. Then two others are needed to replace them, e. g. the purple ones. In a logrolling situation, this would allow the two purple voters to command more money to change their vote than the other electors (black).

A lot of these problems are solved by a proportional list system, a subject for a future Thoughtful Thursday.

As even they admit, they came out strongly in favor of logrolling and point out that side payments among voters are beneficial. Let's go back to the school example. Assume that A and B groups would like a new school system but group C really needs one--either they have more children or their school is crumbling or they just love their children more. Group C can give A or B--whoever wants a school least some money to vote against a school upgrade for their school. In fact, the good doctors say that many of the disorders of majority voting can be solved with side payments or "logrolling." Specifically, those who feel strongly on a particular issue can pay money to those voters who care little one way or the other. On the other hand it does give the wealthy more say so. (This is in contrast to the popular view. Dr. Hansen says that buying is illegal in every state as well as federal elections and refers to the "almost universal condemnation."

For Future Thoughtful Thursdays

Richard L. Hasen, "Vote Buying" California Law Review October 2000, 88 Calif. L. Rev. 1323