De-iri is a Japanese accounting term for income and expenditure that originated during the Taisho era (1912 - 1924).
Deiri counting in Go is one of two main styles of evaluating moves. The other main method is miai counting. Conceptually we judge the value of a play by its size or its urgency. Miai values directly indicate the urgency of plays, while deiri values do so indirectly.
If Black plays first he scores four points, represented as a positive integer, +4.
If White plays first she scores two points, represented as a negative integer, -2.
The deiri value is the difference between these two results (the swing), or 6 points.
We might call the deiri value of a play its swing value.
If Black plays first at a, White must play b to live, and the net score is +2 (Black: 2 points of territory + 2 prisoners; White: 2 points of territory. 2 + 2 - 2 = +2).
If White plays first at a instead, the score is -5. (White: 4 points of territory + 1 prisoner)
The deiri value is the difference between these two results, or 7 points.
We may define deiri values as the difference between the count of the first stable position after Black plays first (called a Black follower) and that of the first stable White follower, assuming normally correct play.
In general the miai value for area scoring is one point greater than that for territory scoring, because you count the stone played as one point. The main exceptions involve seki, because of the differences about counting points for eyes in seki.
If each player makes the same number of moves the extra points by area scoring even out, while if Black makes one more play than White, he gets one more point by area scoring. However, there may be other differences related to seki and ko, depending upon the rule set.
One should use the same kind of scoring for ko threats as for other plays. However, the value of a ko exchange involves not only the size of the threat but also the size of the ko itself and the value of sente.