Today, Parliament is supposed to install the first ad-hoc committee that will evaluate the applicants for the vetting institutions on the basis of two lists drafted by the National Ombudsman and the assessment and recommendations of the International Monitoring Mission (ONM).

Last week, we explained the complicated procedure through which three different parliamentary ad-hoc committees will prepare the final list of candidates that will be voted in Parliament. This procedure is explicated in articles C(10) and C(11) of the Constitutional Annex.

**The problem**

The ONM has given a negative recommendation to 8 of the 29 applicants judged qualified by the National Ombudsman. This leaves 21 qualified applicants. From the 164 candidates judged non-qualified by the National Ombudsman, 85 received a negative recommendation. This leaved 79 applicants who might formally qualify if they produce additional certificates.

Let us assume that the ad-hoc parliamentary committee that is supposed to be installed today by Parliament (unless the opposition decides not to show up), completely follows the advice of the ONM. It requests additional information of the 79 applicants, who all manage to produce the necessary certificates, and the ad-hoc committee votes all of them to the final list of qualifying applicants.

This *optimal* scenario gives us a final list of exactly 100 qualifying applicants for the three vetting institutions.

This list will then go to two new parliamentary ad-hoc committees. One, consisting of 12 deputies, chooses the candidate members of the Independent Qualification Commission (KPK) and Public Commissioners, while the other, consisting of 6 deputies, chooses the candidate members of the Appeals College (KA).

Following the procedure outlined in the Constitution, this process has two steps. We will only consider the first step, the selection of 12 KPK candidate members and 6 KA candidate members. (The candidate Public Commissioners, the 7th KA candidate, and all 6 substitutes are selected by an open vote, whoever gets the most votes wins.)

The first step in both of these ad-hoc committees is that each member selects a single candidate from the list of qualifying applicants through an electronic and secret vote, without prior consultation. In other words, the total of 18 members of both ad-hoc committees do not know from each other which applicant they pick, nor are they allowed to disclose their choice. This means that in theory more than one member can pick the same applicant.

However, the formulation of the Constitution implies that only a selection in which *each* member selects a *unique* applicant – 18 ad-hoc committee members selecting 18 unique candidates for the KPK and KA – is a valid outcome of this first step in the selection procedure.

This brings us to a simple combinatorial question: What is the chance that 18 ad-hoc committee members select 18 unique candidates from a list containing a maximum of 100 qualifying candidates?

**Constitutional mathematics**

In the first part of the election procedure, each deputy in the two parliamentary ad-hoc committees is supposed to select one, unique qualifying candidate. No committee member can choose the same candidate as any other, and they are not able to reveal to each other which candidate they chose, as explicitly prohibited by the Constitution (“without debate through a secret electronic vote”).

We also assume that both committees vote simultaneously (so that they don’t know each other’s election results) and that they only allow one round of voting (as stipulated in the Constitution).

*Calculemus! *

If *all* of the 18 members of the two ad-hoc commissions were able to choose *any* of the qualifying applicants without the necessity that the applicant be unique, the number of possible combinations of 18 candidate members is 100^{18}, that is 100 × 100 × 100 …, eighteen times.

However, of all these 100^{18} possibilities, only those are valid in which no qualifying candidate is chosen more than once. He or she needs to be a unique choice. This means that the “first” committee member has 100 choices, but the “second” only 99, the “third” only 98, and so on.

So the final chance of a *valid *selection of 18 unique candidates after a single secret voting round is therefore: [(100 × 99 × 98 … × 83) / 100^{18} ] × 100% ≈ 19,63%.

Therefore, there is a chance of roughly 1 in 5 that with a maximum pool of 100 qualifying candidates the two ad-hoc committees will successfully elect 18 candidate members of the KPK and KA.

Let us now assume that the first ad-hoc committee only qualifies 8 additional candidates instead of 79. This means that the two ad-hoc committees would be able to choose 18 KPK and KA candidate members from only 29 qualifying applicants. In that case, the chances of arriving at a successful selection in the first round dramatically decreases to only 0.11%!

**A generalization**

A generalized representation of this “constitutional” problem allows us to calculate how many qualifying candidates we need in order to have a high degree of certainty that we get a unique selection of 18 vetting institution candidates within the single round of voting.

If we solve *n* for a certainty of 95%, we would need at a list of at least 2,989 qualified applicants. If we want our chances to be higher then 99%, we would need 15,230 qualifying applicants or more!

**The lesson**

The bottom line is that if implemented according to a strict interpretation of the Constitution, the voting system of the ad-hoc committees becomes highly impractical the lower number the number of qualifying applicants. The electronic voting system would then have to “prevent” that two members vote on the same candidate.

However, such electronic intervention could be interpreted as indirectly sharing information between the different members about their vote, which would therefore no longer be completely secret. If someone votes for an applicant but is “blocked” by the system, they know that another member of the commission voted for the same candidate. Even though the particular committee member would not be revealed, secrecy has been essentially violated.

Another solution would be that committee members don’t choose only one candidate, but provide a list of the 100 applicants ranked from highest to lowest. However, this would mean a violation of the Constitution because 1) the votes of both committees have to be pooled, because otherwise the choices of the two ad-hoc committees could still overlap, and 2) not a single candidate is chosen by each committee member, but a ranking of candidates.

The final solution would be to do multiple rounds of voting, until a “valid” selection of applicants emerges. This would potentially take a lot of time, and would violate the Constitution because only one round of voting is allowed.

In other words, all three solutions to the problem posed by the election of the first 18 members of the KPK and KA necessarily involved the violation of part of the procedure prescribed in the Constitution, either the secrecy of the vote, the nature of the vote, or the number of voting rounds needs to be violated in order for this work out.

Parliament has, yet again, made it very difficult for itself, and the international “experts” overseeing the legislative process clearly didn’t take their math class.

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