RANDOMLY Assigning Powers in Diplomacy

by

Murky

The Problem

A new AFPDip GM wrote to me to discuss a new game which he was interested in running upon afpdip.

The GM wanted to run the game as a 'blind' variant like Io - but with an added twist. The GM wanted the players to be assigned powers randomly. The players needed to be sure that the GM has not influenced the power assignments, and that the players each received a random power. Moreover, each player was NOT to know which power the other players were assigned. However, both GM and player must be able to verify the eventual assignments.

In short:

Powers are to be assigned randomly, without influence from player or GM.
The players and the GM must be able to verify the eventual result.
Each player must be kept in the dark regarding the power assignments of the other players - though not about the identities of the others (though this protocol does not preclude this).

I gave this some thought, and given the following provisos I came up with a solution:

It is only neccessary to prevent unconcious GM bias, if the GM were collaborating with a player then the game has more serious problems than who gets to be Turkey. In other words, this is for where one wishes to be seen to be fair.
I would allow myself a 'third party' when designing the proto player has now received a blinded message, and now adds their own Blinding factor - which they must record. This should be random. Note that each player does not know which message they received due to the GM blinding factor.
Each player sends the message resulting from their blind to a third party, who scrambles the message order at random and once all messages are reveived sends the complete list of messages to the GM. The third party only needs to be trusted enough not to collude with the GM.
The GM now has a list of random looking numbers. Each number is made up of the power allocation message + the GM Blind + The Player Blind. The GM does not know which message is which.
Once the GM has confirmed receipt of this message list the third party asks all the players for their Blinding factors.
The GM subtracts the GM blinding factor, and is then left with messages which are blinded by the players alone.
Once the third party has confirmed receipt of all the blinding factors the GM sends one message to each player. Note that the GM has no way of knowing, even subconsciously, which player is being assigned each power. The GM now publishes the message format, i.e. the verification number and location of the power number, i.e. 4456x464.
The third party publishes the list of the player blinding factors. The players can now try these in turn on their message until they get one in the correct format - this then reveals their power. The GM can do the same.
The player and GM now know who is who, but each player does not know the identity of the others, but does know that their power was assigned without subconcious GM bias.
Phew!

It might seem long winded - and it is, but there are some modifications and helpful program to make it quicker. Firstly lets do an example.
```
Suppose that we the following info:
     Message: 44560464
    GM Blind: 54646487
Player Blind: 87446534 (this is different for every player)
then the GM blinded message would be:
44560464
54646487 +
--------
98106841
Note, numbers have not been carried, i.e. 4+7=1 and not 11
The GM and Player blinded message would be:
98106841
87446534 +
--------
75542375
The message with the GM blind removed would be:
75542375
54646487 -
--------
21906998
The player then tries each player blinding factor, which
have now all been published, and once the player tries 
the correct blinding factor then the original message 
is restored (recognised due to the verification number 
which the GM published)
21906998
87446534 -
--------
44560464 ----> This is power zero, i.e. Austria.
The GM knows the final allocation of all players, 
and the players each know their own allocation,
but nobody could influence who got which alocation
before the messages were revealed.
```
Note, the trusted third party CAN be a player, in this case the player blinding factors would be sent to all players before the GM sent out the power allocation messages - however in this case any one player can 'blow' the scheme by sending the GM the player blinds before the GM sends out the final messages.

In the event of one message being corrupted then this may be recognised and corrected by the GM. If two messages are corrupted then the GM and trusted third party will need to collaborate in order to track the messages - or the protocol will need to run again.

No player, using the above protocol, can see a power and then claim that a message has been corrupted if they don't like it. To fully guard against this the GM might even ask for confirmation of receipt of the final message before the player blinds and message format are revealed.

Note that the GM cannot unconciously bias the results.... Nor can the GM conciously bias the results - but if this is a danger then, as I have said, the game has bigger problems than who plays which power.

In order to help with the addition and subtraction, as accuracy is essential I have w