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Package ‘rSRD’
(2023)
We provide an implementation for Sum of Ranking Differences (SRD),
a novel statistical test introduced by Héberger (2010)
<doi:10.1016/j.trac.2009.09.009>. The test allows the comparison of
different solutions through a reference by first performing a rank
transformation on the input, then calculating and comparing the distances
between the solutions and the reference - the latter is measured in the
L1 norm. The reference can be an external benchmark (e.g. an established
gold standard) or can be aggregated from the data. The calculated distances,
called SRD scores, are validated in two ways, see Héberger and Kollár-Hunek
(2011) <doi:10.1002/cem.1320>. A randomization test (also called permutation
test) compares the SRD scores of the solutions to the SRD scores of randomly
generated rankings. The second validation option is cross-validation that
checks whether the rankings generated from the solutions come from the same
distribution or not. For a detailed analysis about the cross-validation
process see Sziklai, Baranyi and Héberger (2021) <arXiv:2105.11939>. The
package offers a wide array of features related to SRD including the computation
of the SRD scores, validation options, input preprocessing and plotting tools.
The public goods game is a famous example illustrating the tragedy of the commons (Hardin in Science 162:1243–1248, 1968). In this game cooperating individuals contribute to a pool, which in turn is distributed to all members of the group, including defectors who reap the same rewards as cooperators without having made a contribution before. The question is now, how to incentivize group members to all cooperate as it maximizes the common good. While costly punishment (Helbing et al. in New J Phys 12:083005, 2010) presents one such method, the cost of punishment still reduces the common good. The selfishness of the group members favors defectors. Here we show that including other members of the groups and sharing rewards with them can be another incentive for cooperation, avoiding the cost required for punishment. Further, we show how punishment and this form of inclusiveness interact. This work suggests that a redistribution similar to a basic income that is coupled to the economic success of the entire group could overcome the tragedy of the commons.