gab es heute eine Gesprächsrunde zum Thema Wirtschaftswachstum durch Umverteilung? über unser Paper Redistribution Spurs Growth by Using a Portfolio Effect on Risky Human Capital an der ich auch mitmachen durfte.
HK model with heterogeneous bound of confidence and noise
I programmed a model of continuous opinion dynamics under bounded confidence in NetLogo. I hope it can serve as a good demonstration of bounded confidence dynamics. You can play with the model as a JAVA Applet in the Browser (be patient, it takes some initialization time). Or you can download bc.nlogo and run it with your local version of NetLogo (Download NetLogo). The latter improves performance on my computer.
In the model, agents adjust their opinion gradually towards the opinions of others when the distance in opinion is within their bound of confidence. Sometimes agents change their opinion to a new one at random. When agents hold extreme opinions they might never adjust opinions.
The model includes:
- its two main variants of communication regimes (as in Deffuant et al 2000 with μ=0.5 and as in Hegselmann and Krause 2002)
- alternative aggregation of opinions by the median instead of the mean
- heterogeneous bounds of confidence coming from a four parameter beta distribution
- noise via random reset of opinions (as in Pineda et al 2009)
- one-sided and two-sided extremism (similar to Deffuant et al 2002)
In this post (in German) I demonstrated the superiority of the median over the mean in aggregating a good estimate for a guessing questions which answers are bounded by zero but have no upper limit. I speculated further that the correct value often lies slightly above the median. John Doyle recently invented the meandian (see Meandian: A Measure of Location Based on Signed Rank of Deviations) as a measure in between the mean and the median. As a consequence the meandian is typically slightly larger than the median. Doyle showed on our PNAS dataset that the meandian indeed delivers as good results as the median and often better ones.
As I really liked the idea of the meandian, I quickly checked the measure on my “Weisheit der Bremer”-dataset and found:
Truth = 10788, Median = 9843, Meandian = 12170.
Deviations: |Median-Truth| = 945, |Meandian-Truth| = 1382.
Conclusion: Meandian is also good, but the Median wins in this case.
By the way: All are beaten by the geometric mean:
Geomean = 10510 (Deviation |Geomean-Truth| = 278)
Today, Thomas Metz made me aware of a dataset about ministers in Eastern German federal states (Bundesländer) by Sebastian Jäckle. The dataset includes the variable “duration of incumbency” in days for 291 ministers between 1990 and 2011.
I was curious to look at the distribution of duration with the intention to be brave as a physicist and infer a simple stochastic model which reproduces that distribution. I copied the duration data into a matlab vector duration, made histograms, fits for different distributions and KS-Tests. As duration is a discrete random variable (days starting from inauguration), distributions living on the nonnegative integers are the natural candidates. The classical one-parameter distributions Poisson and geometric failed to deliver fitting distributions, but the negative binomial (NB) did surprisingly well.
Normalized histogram for duration of incumbency and best-fit negative binomial probabilty mass function.
The best fit yielded parameters
What model does this imply? Looking at the days in the incumbency of a minister. Let us assume that every day can either be a success or failure which happens with probability . The negative binomial is the distribution of the number of successful days until
failures occur (there is an extension to non-integer number of failures). Our model is thus, that a minister’s incumbency ends after a certain number of failures (what ever that means in practice). The best fit suggests that under this model 1.79 failures are allowed during a minister’s incumbency and that failures are relatively rare events happening with probabilty 0.11% every day, i.e. on average the first failure happens approximately at day 900.
Continue reading ‘Ministers’ incumbency ends after 1.79 failures with daily failing probability 0.11%’
Article in “The Socionomist”