Deaths breakdown by cause

Data source: CDC, National Vital Statistics Reports, Volume 58, Number 19. Deaths: Final Data for 2007. May 20, 2010. Table 10. Number of deaths from 113 selected causes and Enterocolitis due to Clostridium difficile, by age: United States, 2007.

Guicciardini’s Dialogue on the Government of Florence (concluded)

First part here.

Book II

P. 85:

Since cities were founded and survive for no other reason than for the benefit of their inhabitants, which is based principally in preserving the common good, this cannot be restricted to one particular person or individual except at the expense of all the others. So what, I ask you, could be more pernicious or contrary to the essence of a city than for one part of it to be, quite unjustly and for no reason, excluded from all or part of the public benefits and consequently made to suffer greater disadvantages and burdens more than the other?

P. 103:

[A]lthough it [the Venetian government] has a different name from the one we want to use, because it is called a government of nobles and ours will be called a popular government, it is not for this reason of a different type, since it is simply a government in which everybody who is qualified for office participates, making no distinction either for wealth or for family, as happens when the ottimati rule, but all are equally admitted to everything, and they are very numerous – perhaps more so than in ours. And if the plebs don’t participate, the don’t in ours either, since infinite numbers of workers, newcomers to the city and others, do not belong to our Council. And although it is more difficult in Venice for the ineligible to be qualified for office than with us, this is not because the type of government is different, but because within the same type they have different institutions. […] So if we were to call our citizens gentlemen and reserved this title for those who were qualified for office, you would find that the government of Venice is as ‘popular’ as ours and that ours is no less a government of optimates than theirs.

Minor party entry barrier

Elections are first and foremost a mechanism for eliminating non-elite competitors for power – their role as an inter-elite arbitration mechanism is merely a derivative of their primary function. The filtering function is most severe in first-past-the-post systems, where there are often just two credible competitors, and rarely more than 3.

[ Due to typesetting constraints, I am using [ … ] as shorthand for the reciprocal of the expression in the square brackets. That is [ x ] = 1 / x. ]

Within the Tullock contest model, the entry barrier for minor parties can be calculated. The Tullock contest model specifies the chance of party k winning power as p_k = x_k [ t_k ] [ x₁ / t₁ + … + x_{n /} t_n ], where x_i is the amount of resources spent by party i, and t_i is the (in)effectiveness of the party’s campaign efforts.

Each party is characterized by its campaign effectiveness and its fund raising effectiveness f_i. Given the benefits of power, G, the expected return for party k is:

U_k = p_k G – x_k [ f_k ] = x_k [ t_k ] [ x₁ / t₁ + ^… + x_{n /} t_n ] G – x_k [ f_k ].

The model assumes that parties spend the amount that maximizes their expected returns. Under the model assumptions there will always be at least two parties with non-zero expenditures, since a party that finds itself without a spending opponent reduces its spending, until the derivative of the expected return for a competitor becomes positive at 0.

Let z_i = x_i [ t_i ] [ G ], Z = z₁ + ^… + z_n, and r_i = t_i [ G f_i ], i = 1, …, n. Then,

U_k = G ( z_k [ Z ] – r_k z_k ),

And

d U_k [ d z_k ] = G ( (Z – z_k) [ Z² ] – r_k ).

An equilibrium with n parties 1, …, n exists if there exists a solution to the n simultaneous equations,

d Ri [d z_i] = 0, i = 1, …, n,

such that z_i > 0, i = 1, …, n.

If the solution exists, then, summing the n equations:

Z = (n – 1) [ R ],

where R = r₁ + ^… + r_n.

Then,

z_k = Z (1 – r_k Z).

Then z_k > 0 if r_k > [ Z ] = R [ n – 1 ], which is true if and only if

r_k > (R – r_k) [ n – 2 ].

Thus, a solution exists if

min_k r_k = r_(n) > (r₍₁₎ + ^… + r_{(n – 1)}) [ n – 2 ],

and the number of parties at equilibrium will be the maximum number n such that

r_(n) ≥ (r₍₁₎ + ^… + r_{(n – 1)}) [ n – 2 ].

In particular, this implies that any party which has r > r₍₁₎ + r₍₂₎ will have negative benefit from engaging in an election campaign.