First, what happens if subsets of the group meet and some of those parties sway others or reach compromises in order to form coalitions?

Second, taking this idea further, can we investigate a variety of decision processes to find an optimal process for a desired outcome and design coalitions in order to reach a desired outcome?  In terms of the example situation,  this is the problem of finding coalitions that will drive a desired result from those we predicted last time.

Again, here is the prediction from the last post:

party     :    Pos        Inf(Norm)    Sal
-----------------------------------------------
d2        :    15        0.03774        80
ctcust    :    35        0.09434        5
ctsal     :    35        0.03774        5
er        :    50        0.01887        20
eng       :    60        0.07547        99
me        :    75        0.15094        99
d1        :    75        0.15094        99
adv       :    100       0.15094        20
legal     :    100       0.13208        95
inv       :    100       0.15094        5
-----------------------------------------------
Position (weighted avg):        76.4
Position (balance of power):    71.7

TABLE 1

To answer the first question, we need to build a simple model that replaces a coalition with a single new entity. In the model, the choice was to add the Influence of the parties of a coalition.  The new position was the weighted average of the positions as described before.  For the Salience, we need to reflect the idea that the most interested party in a coalition will drive the others and use their influence to support the new positions but with some skewing toward their Salience.  To model this simple, replace the new entity’s salience with 20% of the average Salience + 80% of the max Salience.  Many other choices can be made and explored using the tools here.

To answer the second question, we need a way to generate all of the possible coalitions.  This amounts to generating a set partitioning of all the parties.  TABLE 2 shows a simple example with only 4 parties.

Parties    :     ['a', 'b', 'c', 'd']

<<<  15 Partitions  >>>
-----------------------------
[['a', 'b', 'c', 'd']]
[['a', 'b', 'c'], ['d']]
[['a', 'b', 'd'], ['c']]
[['a', 'b'], ['c', 'd']]
[['a', 'b'], ['c'], ['d']]
[['a', 'c', 'd'], ['b']]
[['a', 'c'], ['b', 'd']]
[['a', 'c'], ['b'], ['d']]
[['a', 'd'], ['b', 'c']]
[['a'], ['b', 'c', 'd']]
[['a'], ['b', 'c'], ['d']]
[['a', 'd'], ['b'], ['c']]
[['a'], ['b', 'd'], ['c']]
[['a'], ['b'], ['c', 'd']]
[['a'], ['b'], ['c'], ['d']]

TABLE 2

For 10 parties, there are 115,974 games to play out.  (See Donald Knuth’s The Art of Computer Programming Vol 4 F3).  You can download output of all 115,974 games.  The interesting games are the extremes: the game that results in the maximum position and the one that results in the minimum position.

Game A
maxPos : 83.22147
party                           :    Pos        Inf(Norm)    Sal
----------------------------------------------------------------
eng                             :    60        0.07547        99
_d1+d2_                         :    64        0.18868        95
_er+me_                         :    74        0.16981        83
_adv+ctcust+ctsal+inv+legal_    :    97        0.56604        77
-----------------------------------------------------------------
Position (weighted avg):    83.2
Position (balance of power):    77.1

(Game # : 2089)

Game B
minPos : 66.27527
party                    :    Pos        Inf(Norm)    Sal
------------------------------------------------------------
_ctcust+ctsal+d2+inv_    :    32        0.32075        65
_d1+eng+me_              :    72        0.37736        99
_er+legal_               :    98        0.15094        80
adv                      :    100       0.15094        20
------------------------------------------------------------
Position (weighted avg):    66.3
Position (balance of power):    51.2

(Game # : 47615)

TABLE 3

In Game A, a coalition of d1+d2 and er+me results in the most extreme high-number position. The final position realized was 100 and these two coalitions were instrumental in the outcome.  To design for to most extreme high position, these are the coalitions to nurture.

In this case, however, d2, the biggest stakeholder in the low-number position, would have achieved more of their goals had they designed the decision process around the coalitions shown in Game B.  By building a relatively strong coalition around ctcust+ctsal+d2+inv and a diffusive coalition around er+legal, a much lower position is achieved.

There is a second hint here too.  If the decision process could be more focused on Balance of Power rather than a salience/influence weighted average, a position of around 50 might be reached.   This might be done, for example, by getting all the parties to agree to a final vote with 1 vote per person, winning position takes all votes, then voting in rounds sequentially through the coalitions of Game B top to bottom.

Download the Python model modules: MultiPlayerGame.py MultiPlayerNegotiationsModel.py Partitioner.py

I recently had the opportunity to observe a business negotiation between about a dozen parties that seemed ripe for PG analysis. Among the basic ideas explained in the book are the basic inputs used by De Mesquita’s models and how to make estimates of “game” outcomes.  In a future post the model here will be expanded to model more of the details of interactions between the parties and sub-groups. As the book contains few hints to how De Mesquita does this, those models will be striking off on our own.

But first, back to the negotiations and simple estimates of the outcome. All of the parties below are actual people involved in the negotiation.  Negotiations covered about 2 months and are completed with respect to these positions.

The object is to calculate two estimates of the outcome of the negotiations following Predictioneer’s Game. Here are the steps:

(1) Identify the stake-holding parties involved in the negotiations.  Anyone who takes a definite position and has some stake in the outcome should be included.  This model includes only the most obvious players.

Party     [Position, Influence, Salience]
-----------------------------------------
    data = {
        'd2':       [ 15,  20,  80],
        'ctcust':   [ 35,  50,   5],
        'ctsal':    [ 35,  20,   5],
        'er':       [ 50,  10,  20],
        'eng':      [ 60,  40,  99],
        'd1':       [ 75,  80,  99],
        'me':       [ 75,  80,  99],
        'adv':      [100,  80,  20],
        'inv':      [100,  80,   5],
        'legal':    [100,  70,  95]
    	}
     		TABLE 1

(3) Describe the relative influence of the parties.  Below, the influence will be normalized to add up to 100%, so just choose a scale that is convenient to get the relative numbers right.  In the example, I estimated the influence of each party at the same time as I estimated positions.

(4) Now it is time to the estimate cost/benefit to each party.  Salience is a score starting with ambivalence=0 moving up to everything there is to gain or loose is staked on the outcome scoring 100.

Predictioneer’s Game describes students and analysts researching positions and salience for political problems through interviews, CIA analyst records, newspapers, eye-witness reports etc.  These steps could take a great deal of work.  But also some discipline to hear and interpret what people are trying to accomplish.

Time to estimate outcomes. The first estimate is the weighted average position given by

Plugging in the numbers above gives a position just above parties d1 and me at 76.4. See Table 2 below.

The second estimate of outcome is the point along the position line where the cumulative total influence is 50%.  That is, there is as much influence pulling the final position to the left as to the right.  In this case the the balance-of-power point is at position 71.7.

The results are summarized on the table below.  Influence has been normalized to add up to 100%.

Party   :       Pos             Inf(Norm)       Sal
------------------------------------------------------------
d2      :       15              0.03774         80
ctcust  :       35              0.09434         5
ctsal   :       35              0.03774         5
er      :       50              0.01887         20
eng     :       60              0.07547         99
me      :       75              0.15094         99
d1      :       75              0.15094         99
adv     :       100             0.15094         20
legal   :       100             0.13208         95
inv     :       100             0.15094         5
------------------------------------------------------------
Position (weighted avg):        76.37
Position (balance of power):    71.72

		TABLE 2

Both of these predictions give a position that was discussed as a plausible compromise between the more extreme positions.

This is not how the negotiations worked out.  The final outcome was at position 100.  In fact, the middle ground evaporated about 7 days after I first made this calculation.  This situation moved very quickly to position 100 with everyone from position 50 and above accepting the 100 was the only possible outcome and the majority of the influence below position 50 also insisting that, although undesirable, 100 was the only possible outcome.

I am fairly confident that any proposal from the influential parties in the positions below 50 that landed at or slightly above 50 would have lead to further negotiations and resolution.  In this case, some of the parties decided not to fight for their positions directly. This means I overestimated the salience of their positions?