Party affiliation and general outlook 1991-2011
May 24, 2011
The proportions of Americans who are politically affiliated with one of the two major parties has been very stable over the last 20 years, at about 60% with a slight downward trend (+ marks and thick trend line in the chart below). Over the same period, the general outlook of the public has fluctuated wildly, with those who say the country is “going in the right direction” reaching over 50% at one point and falling 5 years later to 20% (circles and thin trend line). The public mood seems to be optimistic immediately following presidential elections (vertical dashed lines), and pessimistic immediately before them.
Data source: New York Times/CBS poll, April 15-20, 2011.
Sliding window statistics calculation complexity
May 11, 2011
The following C++ code takes a sequence of n elements, a1, a2, …, an, and outputs a sequence of n – k + 1 elements. The i-th output element is a maximal element in the subsequence ai, ai + 1, …, ai + k – 1. The runtime complexity of the code is O(n).
template <typename T>
void insert(std::list< std::pair<T,unsigned int> > &l, T v)
{
unsigned int sp = 0;
while (!l.empty() && l.back().first < v)
{
sp++;
l.pop_back();
}
l.push_back(std::pair<T,unsigned int>(v,sp));
}
template <typename T>
void advance(std::list< std::pair<T,unsigned int> > &l)
{
if (l.front().second > 0)
l.front().second--;
else
l.pop_front();
}
template <typename T>
void max_in_window(T const *in, T *out, size_t n, size_t k)
{
std::list< std::pair<T,unsigned int> > l;
unsigned int i;
for (i = 0; i < k - 1 && i < n; i++)
insert(l,in[i]);
for (; i < n; i++)
{
insert(l,in[i]);
out[0] = l.front().first;
out++;
advance(l);
}
}
Interestingly, an algorithm for the median in a sliding window will have runtime of at least O(n log k), since such an algorithm can be used to sort O(n / k) sequences of length O(k) each:
Let a1, a2, …, an be a sequence of numbers in a known interval, say (0, 1). Create a sequence of length 3n – 2 by padding the sequence with a prefix of (n – 1) 0‘s and a suffix of (n – 1) 1‘s. Now execute the sliding window median algorithm with the padded sequence as input, and with k = 2n – 1.
The i-th output element will be the median of a sequence that is made of the entire sequence a1, a2, …, an, n – i zeros, and i – 1 ones. That median is a(i), the i-th smallest elements of the sequence a1, a2, …, an. Thus, the output of the algorithm will be the sorted sequence a(1), a(2), …, a(n).
Medical Doctor degrees conferred in the U.S.
April 18, 2011
The number of Medical Doctor degrees conferred in the U.S. has remained unchanged since 1985 – about 15,000 degrees a year. Therefore, the number of MD degrees conferred per U.S. resident has fallen since 1985 by the same rate as the growth of the population – about 25% cumulatively.
That period has also seen a significant increase in the median MD earnings, as measured by the BLS (Current Population Survey – CPS, Weekly & Hourly Earnings): In the decade between 2000 and 2010, physicians and surgeons have seen their nominal median income increase 51%, while lawyers saw an increase of 37%, and the average worker saw an increase of 30% (series LEU0254541000, LEU0254536800, LEU0252881500). The 30% increase, incidentally, represents a 2.5% inflation-adjusted increase according to the BLS.
Data source: Statistical Abstract of the U.S. 2011 edition, Table 300 (spreadsheet); 1980 edition, Table 293.
Supreme intellectual achievement
March 17, 2011
Ricardo offers us the supreme intellectual achievement, unattainable by weaker spirits, of adopting a hypothetical world remote from experience as though it were the world of experience and then living in it consistently. With most of his successors common sense cannot help breaking in — with injury to their logical consistency.
John Maynard Keynes,
The General Theory of Employment, Interest and Money, Appendix to Chapter 14
Deaths breakdown by cause
February 28, 2011
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)
February 16, 2011
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
February 8, 2011
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 pk = xk [ tk ] [ x1 / t1 + ... + xn / tn ], where xi is the amount of resources spent by party i, and ti is the (in)effectiveness of the party’s campaign efforts.
Each party is characterized by its campaign effectiveness and its fund raising effectiveness fi. Given the benefits of power, G, the expected return for party k is:
Uk = pk G – xk [ fk ] = xk [ tk ] [ x1 / t1 + ... + xn / tn ] G – xk [ fk ].
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 zi = xi [ ti ] [ G ], Z = z1 + … + zn, and ri = ti [ G fi ], i = 1, …, n. Then,
Uk = G ( zk [ Z ] – rk zk ),
And
d Uk [ d zk ] = G ( (Z – zk) [ Z2 ] – rk ).
An equilibrium with n parties 1, …, n exists if there exists a solution to the n simultaneous equations,
d Ri [d zi] = 0, i = 1, …, n,
such that zi > 0, i = 1, …, n.
If the solution exists, then, summing the n equations:
Z = (n – 1) [ R ],
where R = r1 + … + rn.
Then,
zk = Z (1 – rk Z).
Then zk > 0 if rk > [ Z ] = R [ n - 1 ], which is true if and only if
rk > (R – rk) [ n - 2 ].
Thus, a solution exists if
mink rk = 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.
Guicciardini’s Dialogue on the Government of Florence
January 30, 2011
Original text written in the 1520′s.
Translated by Alison Brown.
Book I
P. 35:
I have often wondered on the fact that this word ‘liberty’ is frequently used more as a disguise and an excuse by those who want to conceal their cupidity and ambition than because men in fact have a natural desire for it. I am talking of the liberty we think about in governing a city, not the liberty that concerns individuals, that is, whether a man is free or enslaved. It seems to me, unless I’m mistaken, that men have a natural desire to dominate and be superior to others; there are normally very few people who love liberty so much that if they had a chance to make themselves lords or superior to others they would not do so willingly. [...] But men often let themselves be so deceived by names that they do not recognise the things themselves; and so,when the name of liberty is repeatedly invoked in civil conflicts, most people are blinded by it an do not realise that the objective is different.
Those who enjoy leading positions in the city do not primarily seek liberty as their objective as much as increase of power and making themselves as superior and outstanding as possible. As long as possible, they strive to conceal their ambition with this pleasing title of liberty. This is because those in a city who fear being oppressed far outnumber those who hope to oppress, so the person who seems to be assuming the patronage of equality has far more supporters than someone who openly goes for superiority. Nevertheless, if successful, the outcome reveals the designs of such men, since it is through this deception that they generally use the multitude to make themselves great. [...] On the other hand, the people desire and choose liberty as their objective. This is because the position of the majority is such that they fear being oppressed or enjoying a reduced share of the honorary and the salaried offices in the republic, so that the first thing they must concentrate on is equality[.]
