v0.9 | 2018-03-xx | 1375 words | Doug Webb

Cooperative Decision Making


Three features of cooperative voting systems are put forward:

  1. the inclusion of an option to ‘find other options’ by default,
  2. the ability for participants to expressively score each option, and
  3. the appropriate multiplication of negative scores before tallying.


Just as the present has been shaped by the decisions of the past, so too do the decisions we are yet to make shape the future. On the basis that how decisions are made influences what is decided, an important question for those wishing to find themselves in a more cooperative future is how can we decide more cooperatively?

Often ‘cooperation’ is used to describe conflict-free compliance. Here cooperation is used more boldly to describe a quality of interaction which supports, and arises from, personal autonomy, interpersonal equivalence and mutual interest.

A method of decision-making can be said to respect autonomy if it allows each affected member of a group to meaningfully and directly participate. For any sizeable group this requires a formal procedure which specifies how participants can express their opinions on a set of options, and how participant opinions are combined to select from these options: procedures fitting this description are commonly called voting methods. In contrast are methods based on random chance (e.g. lottery) or those in which some decide for others (e.g. dictatorships.)

A voting method can further be said to respect equivalence if it values participants equally, as summarized by the principle one person, one vote. A counterexample is seen in stock-owned companies where share-holders receive voting power proportional to their share size. However, a voting method which respects equivalence does not necessarily respect mutual interest.

Consider a group of people who are deciding whether to paint their bike-shed Blue, Red or Green. They vote by each choosing one option and selecting the most chosen option (i.e. a relative majority/plurality vote.) Blue wins by a narrow margin, an outcome quite unacceptable to the large minority which voted Green. However, Blue-voters and Green-voters find Red to be acceptable and both would have preferred it—despite it not being their first personal preference—since they share a mutual interest: that Red wasn’t chosen demonstrates that the method was inadequate to respect mutual interest.

Thus a voting method can be said to respect mutual interest by making a selection which values acceptance over preference. Some methods attempt to do this by allowing participants to veto proposals (e.g. unanimous consent or consensus) with the reasoning that no participant need endure a decision they find unacceptable. However, if the option to veto is viewed positively as the option to change nothing then a single voter who prefers things the way they are is in a position of dictatorial power to select their preferred option regardless of how (un)acceptable the others find it.

Given this exploration into what cooperative voting is and isn’t considered to be, specific features for each aspect of a voting system are reasoned in turn: the available options, expression of opinions and combination of opinions.

Options: an acceptable one for everyone

The outcome of a vote is restricted to the options available at the time of voting. Since there is always the option to change nothing (i.e. continue with the status quo,) only one alternative option must be proposed.

However most decisions are not binary; there is almost always more than one alternative for any situation, usually an overwhelming number. Since only a fraction of alternatives can be made available for a vote, it is possible that the ‘best’ option for a group is not among them. Worse still, some voters could find none of the available options to be acceptable and thus be forced to vote for the lesser evil.

Hence the first feature of cooperative voting is to include the option to ‘find other options’. Providing a way for people to vote again on different options essentially allows people to vote on every option, including options not yet conceived; this ensures that there is always an acceptable option for every participant.

a diagram representing the expansive nature of the 'find other options' option

Expression: getting the whole picture

People must be able to express themselves in a way that is simple enough to be easily combined later, yet complex enough to communicate acceptance and preference.

When voters are only allowed to select one option (i.e. plurality) they express nothing about the other options. Even methods which allow voters to rank all options in order of preference (i.e. ordinal methods,) voters cannot express whether they hold a positive, neutral or negative opinion toward a particular option: does someone like or dislike an option they voted third out of five? Additionally both plurality and ordinal methods can actively encourage voters to tactically misrepresent their preference order to secure a better personal outcome whenever there are more than two options available (Arrow, 1963), precisely the situation caused by putting the first feature of cooperative voting in place.

While no voting system is free from the possibility of tactical voting in the presence of three or more options (Gibbard, 1973), scoring methods (i.e. cardinal methods) encourage fewer distortions, most notably they never encourage voters to misrepresent their preference order. Even more importantly, scoring option allows the selection of the context of cooperation, scoring options allows voters to express acceptance and preference. Using a symmetrical range of positive and negative numbers, voters can indicate the degree to which they find options (un)acceptable with negative scores, and the degree to which they acceptable options preferable with positive scores.

Hence the second feature of cooperative voting is to allow participants to score each option from an expressive range. A range of less than 10 points is recommended for cognitive ease, verbal or pictorial indicators can be used to clarify what is meant by the numerical values.

a graphical comparison of plurality, rank and score methods

Combination: acceptable, achievable outcomes

To reach a decision which upholds mutual interest, scores should be combined in a way that values acceptance over preference. This requires something other than direct addition, since allowing positive scores to cancel out negative ones (e.g. +3 + -3 = 0) equates the value of acceptance with preference. A simple way to achieve the difference in valuation is to increase the weight of negative scores before totalling.

This approach reflects the philosophical intuition that “human suffering makes a direct moral appeal, namely, the appeal for help, while there is no similar call to increase the happiness of a person who is doing well anyway” (Popper, 1945). A practical advantage with this approach is that options with higher levels of acceptance will be selected; these are less likely to cause later conflict and are therefore more likely to be realized.

However, considering negative scores to be ‘infinitely’ more important than positive ones is problematic. As a philosophical position this implies that an outcome which everyone is completely neutral towards is preferable to one which everyone strongly prefers except one who finds it mildly unacceptable. The practical issue with this approach is that options towards which voters have insufficient intrinsic motivation may not happen in cooperative groups, where those who execute are the same as those who legislate.

Hence the third feature of cooperative voting is to appropriately multiply negative scores. This factor represents an exchange rate between positive and negative opinion which is likely to differ between groups. It should at least be larger than 1 to value acceptance over preference and less than the number of group members to make positive scores meaningful: a factor of two may be an appropriate starting point.

a scale with a sad emoji weighing more than a happy one

An example: back to the bike-shed

The group that earlier voted to paint their bike-shed Blue are unsatisfied with the result of their initial method. They vote again using a method with the features of cooperative voting described above: they list the options “Change nothing: leave it unpainted” and “Find better options: vote again in a week” alongside the previously identified options Green, Red and Blue; they score using a three-point scale (+1, 0, -1) and they multiply negative scores by a factor of two before totalling scores. This time, without voter opinions changing, Red is selected: a more cooperative outcome.