The Arithmetics of Election Rigging in Nigeria
Mobolaji E. Aluko
Thursday, May 22, 2003
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
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
In the presence of rigging, this "rigging nullification" is the most desirable
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
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
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
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
Best wishes all.