The Arithemetic Of Election Rigging.

A.  INTRODUCTION

Suppose two candidates X and Y go into a free election (that is most or all who wish to register are registered; most or all who registered are allowed to vote) and fairly-counted election.  If X + Y voters are sighted at the polls, and assuming no bad ballots,  if X voters actually voted for X and Y voters actually voted for Y, then X wins if X is greater than Y, Y wins if Y is greater than X and there is a tie X = Y. 

Note that the equality of sighting and total vote counts account for the fair-counting disposition.  The freeness and fairness of any election come from appropriate registration, voting and counting - as well of course as accurate announcing.

B.  THE ARITHMETIC INEQUALITIES

B.1  No Rigging Exists

The magic quantity (win/loss determinant) is dWxy:

dWxy = X - Y    

Case A: X wins, Y loses:  dWxy > 0; 
Case B: X loses, Y wins: dWxy < 0;
Case C:  a tie: dWxy = 0

B.2  Rigging Exists

Now suppose each of X and Y "rig" their own votes by amounts dRx and dRy respectively.  Then, the new magic win/loss determinant is dWxy,r:

dWxy,r = (X + dRx) - (Y + dRy)
             = (X - Y) + (dRx - dRy)
             = dWxy + dRxy

The effect of rigging on a free and fair election is obviously therefore a case of the sign and size of dRxy relative to dWxy.

Case 1:  dRxy = 0; 

i.e.  dRxy has no size, hence no sign.

This is either because

Case 1.1:  dRx = dRy = 0 (no rigging whatsoever) or

Case 1.2  dRx = dRy (equal rigging).

In either case:

      dWxy,r = dWxy

and hence there is absolutely no effect of rigging on the free-and-fair election.

In the presence of rigging, this "rigging nullification" is the most desirable outcome.

Case 2:  dRxy has the same sign as dWxy.

In this case, X's win or loss is not changed by the rigging ('the wishes of the people are preserved"), but the win or loss is enlarged in either case, ie:

   Magnitude (dWxy,r) > Magnitude (dWxy)

That is, the winner who would have won even in a free-and-fair contest has now rigged even more than the loser who would have lost.  There is of course the possibility that the loser may have actually refrained completely from rigging - or was completely prevented from rigging; dRy = 0.

There are two pieces of logic in Case 2:

(1) the winner presents a view of popularity greater than he actually is, and
presents the loser as far less popular than he really is.

(2) in the special situation where the loser did not rig at all, the winner presents an immoral side of himself (assuming rigging is considered immoral) that the voters might have frowned upon had they known that he would rig and his opponent would not/did not (assuming that the case was that it was not because he did not try to rig, but was merely prevented from doing so.)

Case 3:    dRxy has a different sign from dWxy

This is the case where things start to get complex, because there are many subcases here.

Case 3.1:  Magnitude (dRxy) < Magnitude (dWxy)

In this case, the win or the loss of the candidate is also not changed ("the wishes of the people are still preserved")  However, the winner's margin is diminished and the loser's loss is also diminished.

The two pieces of logic in view here are that:

(1) the winner presents a view less popular than he really is and the loser presents a view more popular than he really is, even though both would remain winner and loser in a free-and-fair election.

(2) It may be a situation where both candidates have agreed not to "rock the boat", with a concession that the winner should still win, but the loser should be made to look "as good as possible."

Case 3.1 happens in a number of situations in Nigerian elections, when an "arrangee" situation has been done by the candidates/agents of opposing parties to "allocate" votes to each other without upsetting who actually wins.  This is usually done with an eye to ensuring that the total votes reflect some census totals.

Case 3.2:  Magnitude (dRxy) > Magnitude (dWxy)

Aha!  This is where the results of the free-and-fair elections are completely reversed:  the winner becomes the loser and the loser becomes the winner!  The "winner" has rigged so much that he overwhelms he wishes of the people, torpedoeing them completely.  In fact, dWxy,r "phantoms" determined who won and who lost, rather than X + Y persons.

The winner would really be representing dWxy,r phantoms - a ghost electorate.

Note that there are two subcases here:

Case 3.2.1:  X = 0, Y = 0   ie no elections

This is a completely rigged election.  There is no pretence to freeness and fairness,  and usually one of the riggers has "cooked" both rigged numbers (Rx and Ry) to favor (invariably) the winner.

The logic here is that the elections were not really necessary, and so all pretence to lining up to vote should be discarded.

Case 3.2.2:  X .NE. 0; Y .NE. 0  ie there are elections.

The logic here is also that elections were not really necessary, but the pretence to lining up to vote should be allowed.

Case 3.2.2 is, to this writer, more insidious than Case 3.2.2 because it requires both pretence and deceit.

Case 4:  When there is a tie:  X = Y (dWxy = 0) AND dRxy .NE.0

In the case of when there is a tie in a free and fair election, it is then again COMPLETELY the rigged votes - like when there were no elections (Case 3.2.1) -  that determine who wins and who loses.

C.  WHY THE ABOVE ANALYSIS

I have gone into the above analysis to identify the cases and sub-cases so as to urge our Nigerian compatriots to be more specific as to which kind of rigging that they are willing to support, and which ones that they are willing to "move on" over.  I doubt if any moral person would support or tolerate Case 3.2 rigging or Case 4 rigging for that matter.  I can see why people would be tolerant of Case 3.1 rigging, or even Case 2 rigging.  

But how can we know which case to support or move on over if there is charge of rigging, and if there is no Tribunal pronouncement on the type of rigging?

That is the purpose of the tribunals, and those seeking tribunal intervention what they would tolerate and whether they should move on should not be demonized.

As for me and my household, I am only tolerant of Case 3.2 rigging, which is the rarest of events - like the Blue Moon.

D.  EPILOGUE - SOME PERTINENT QUESTIONS

One may ask:  does it really matter what ultimately dWxy is if in fact registration had not been free and fair (eg differential access to information about registration sites/differential access to education), actual ability to vote had not been free and fair (differential access to polling booths/selective rejection of ballots)?

It is a question that is actually quite valid, and should task the mind of pragmatists, who should then determine for themselves their own thresholds for "substantial pre-election compliance."

Another question with an eye to allegations against Abiola (over post-June 12, 1993) and Buhari (over post-April 19, 2003):  does it matter, should our support for or against rigging depend on whether the person who won or lost, that is the victim of rigging or a beneficiary of the rigging was a prior business crook, a womanizer, a coup plotter, an Islamist bigot or a cruel tyrant?

It should not.  Those considerations should go only into the numbers X and Y, and should not determine our negative disposition to non-zero values of dRx and dRy.

Best wishes all.