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Group Mutual Support (Tax Rates)

To quantify mutual support, I defined Tax Rates and a Group Treasury.  After each encounter, a proportion of the gain (or loss) sustained by Self (the Tax Rate) is transferred to the group (the Group Treasury).  The Group Treasury, after the end of the simulation, is then equally divided among all group members.  Thus, the final gain of each group member (Adjusted Self-Gain) is a function of all other members’ gain.

This mutual support can be further defined by two, interrelated dimensions:

1) Equal vs. Unequal Tax Rates among group members

2) High vs. Low Tax Rates

Unequal vs. Equal Tax Rates

Unequal Tax Rates generated many unethical outcomes.  Most were a consequence of Free Riders, group members who take advantage of the others.  The Free Riders contribute little to the group, yet reap benefits from their membership.

When Tax Rates were unequal, the Group Treasury did not significantly rise above zero.  At the end of the series of encounters, there was no wealth to be redistributed among group members.  The Total Adjusted Self-Gain for the group was lower than the Equal Tax Rate groups.  And there was a greater spread of Adjusted Self-Gain for the individuals within the group (less equality in outcome).  Adjusted Self-Gain itself was no greater than Individual Self-Gain.

Agents with High Tax Rates had little or no incentive to make choices that generate Self-Gain.  Knowing that most or all of their gain would be taken from them, they generated near-zero Gain (or even tolerated Loss).  So Agents with High Tax Rates contributed nothing to the Group Treasury.  Conversely, Agents with Low Tax Rates had incentive toward Self-Gain.  But little or none of their gain was transferred to the Group Treasury.  So in the end, no Agents made significant contributions to the Group Treasury.

Agents with High Tax Rates made little or no gain.  Agents with Low Tax Rates could make higher than expected gains (they faced no competition when encountering a High Tax Rate Agent), but that extra gain was not enough to compensate for the loss suffered by High Tax Rate Agents.  So the Total Adjusted Self-Gain for the group was greatly reduced.  An Unequal Tax Rate group gained less than an Equal Tax Rate group, and even less than a no-group population. 

Moreover, because High Tax Rate Agents gained far less than expected, while Low Tax Rate Agents gained slightly more than expected, the spread (in Self-Gain) among group members was even greater than a no-group scenario.  The complementary metric for Total Ethics, Equality, also suffered in an Unequal Tax Rate group.  This was also a consequence of encounters between no-gain High Tax Rate Agents and higher-gain Low Tax Agents.

Unequal Tax Rate groups exhibited a paradoxical effect – they had greater Other-Gain than Equal Tax Rate groups.  At first glance, this would appear to be a step toward a better Total Ethics.  But the underlying reality was the opposite.  Again, it was encounters between High Tax Rate Agents and Low Tax Rate Agents than generated this effect.  A High Tax Rate Agent makes no effort to obtain Self-Gain, allowing Other, the Low Tax Rate Agent, to obtain even greater Other-Gain than expected.  But the increase in Other-Gain was much less than the decrease in Self-Gain.  So the Low Tax Rate Agent was making a gain at a greater expense to the High Tax Rate Agent and to the Group Treasury.  (The High Tax Rate Agents know that Self-Loss will be mitigated by transfer to the Group Treasury).

This paradoxical effect was amplified if the High Tax Rate Agent also possessed Good Will  The High Tax Rate Agent has no incentive toward Self-Gain, and actually has extra incentive toward Other-Gain.  But the increase in Other-Gain is still rendered unproductive by the greater loss to Self and the Group Treasury.  Another consequence to this tax differential is even less Equality of outcome.

Unequal Tax Rates, already generating less Total Ethics, had a counter-intuitive effect on Good Will.  Normally, we would expect Agents with Good Will to generate greater Ethical Outcomes (greater Commonwealth and Equality).  But the effect was exactly the opposite.  Good Will generated more Other-Gain, but only at the greater expense of Self-Gain and the Group Treasury, lowering the Total Adjusted Self-Gain of the group.  Good Will also generated less Equality of outcome.

The Equal Tax Rate groups avoided many of the pernicious effects of differential Tax Rates.  With no Free Riders, all members made equal contributions to the Group Treasury.  Consequently, the Group Treasury was significantly greater than zero.  Agents received some benefit from group membership, in that Adjusted Self-Gain was greater than Individual Self-Gain.  And there was more Equality of outcome among group members.  There was less spread among the members’ Adjusted Self-Gain, and the average encounter generated greater Equality than the Unequal Tax Rate groups.  Significantly, the actual Tax Rate, be it Low or High, had no effect on Equality of outcome.

Other-Gain was less than that of the Unequal Tax Rate groups, but also less than no-group populations.  With Equal Tax Rates, there was no incentive to favor one agent over another, which caused the artificial Other-Gain in the Unequal Tax Rate groups.  However, Tax Rates greater than 0% suppressed Other-Gain.  An Agent with Good Will had less incentive to cede gain to Other.  Knowing that a proportion of Other’s Gain would be transferred to the Group Treasury (taxed), a Good Will Agent was less likely to make a choice to generate Other-Gain.  An Equal Tax Rate group, especially one with a High Tax Rate, generated less “true” Other-Gain.

Non-zero Tax Rates, even when equal, still suppressed Total Adjusted Self-Gain.  As the Tax Rate increased, there were diminishing returns to the Group Treasury.  As the Tax Rate increased, both Agents had less incentive to make choices for Self-Gain.  Their joint loss lowered contributions to the Group Treasury, and lowered Adjusted Self-Gain.  These same incentives also generated a slight increase in Equality.  With neither Agent striving for gain, both Self-Gain and Other-Gain tended toward zero, making them more equal.

Equal Tax Rates alone did not generate a better Total Ethics than a no-group scenario (Total Adjusted Self-Gain still was lower), but they were far superior to the deleterious effects of Unequal Tax Rates – far lower Total Adjusted Self-Gain, a greater spread in Self-Gain, less Equality, and the counter-productive effects of Good Will.

High vs. Low Tax Rates

High Tax Rates also generated less Total Ethics, but their effects were not as bad as Unequal Tax Rates.  High Tax Rates lowered all metrics of Self-Gain (Individual, Adjusted, and Total Adjusted), even within an Equal Tax Rate scenario.  The disincentives were the same as described above.  An Agent with a High Tax Rate had less incentive to make choices for Self-Gain.  Where all Agents have a High Tax Rate (or even a non-zero Tax Rate), there was less gain for the group.  The Group Treasury rose with a Higher Tax Rate (assuming Equal Tax Rates), but only with diminishing returns.

Even with Equal Tax Rates, High Tax Rates will diminish both Other-Gain and Commonwealth.  Agents with Good Will will have less incentive to cede gain to Other, knowing that gain will be transferred to the Group Treasury.

Where Tax Rates are unequal, Agents with High Tax Rates will suffer in several ways – unable to generate Self-Gain, less Equality of outcome, and an artificially high Other-Gain subsidized by an even greater Self-Loss.  Agents with Low Tax Rates will benefit from encounters with High Tax Rate Agents, but only at a greater expense to the High Tax Rate Agent and the group.  These same Low Tax Rate Agents will have no incentive to generate Other-Gain, even if they possess Good Will.  They perceive any gain made by the High Tax Rate Agent to be transferred to the Group Treasury.

High Tax Rates have a dampening effect worth noting.  As described on other pages, some Basic Strategies (Best Row, Minimize Loss) are very effective in generating Self-Gain, even under adverse circumstances.  However, they lose their effectiveness as the Tax Rate increases.  At the very highest Tax Rate, 100%, all Basic Strategies are equally unproductive.  They all generate an average Self-Gain of zero.  The best Self-Gain strategies are no more effective than random choices when all gain is transferred to the Group Treasury.  So the relative effectiveness (the ranking) of the Basic Strategies becomes irrelevant as the Tax Rate increases.