A mathematical model to assess where each candidate stands
By Javier Surasky
Date drafted: 21/08/2026
Introduction
Today, the United Nations Security Council held its second straw poll as part of the informal process to choose the next head of the UN Secretariat.
Here, I apply to its results the
calculation used to assess each candidate’s chances mathematically, following the formula presented and described in the analysis of the first straw poll,
where we also set out its assumptions and limits. It is important to note that
we still do not know which votes were cast by permanent members, something
that, as we explained in that blog, is critical to giving the model’s results
greater certainty.
What do the results of the second straw poll tell us?
The vote in the second straw poll gives us
the following table, which includes for the first time the candidate Ivonne
A-Baki, an Ecuadorian of Lebanese descent, recently put forward by Tonga and
known for her public statements in support of Donald Trump.
The result is shown in the following table
|
Candidacy |
E |
D |
N |
|
Carolyn Rodrigues-Birkett |
8 |
3 |
4 |
|
Rebeca
Grynspan |
7 |
4 |
4 |
|
Rafael Mariano Grossi |
7 |
6 |
2 |
|
Macky
Sall |
6 |
7 |
2 |
|
Olara Otunnu |
5 |
5 |
5 |
|
María
Fernanda Espinosa |
4 |
3 |
8 |
|
Michelle Bachelet |
2 |
6 |
7 |
|
Ivonne
A-Baki |
0 |
8 |
7 |
In an initial comparison between the first
and second straw polls, several interesting points emerge: Rodrigues-Birkett
moves into first place despite losing one vote of support compared with the
previous round, because Grynspan, who had received the largest number of
favorable votes in the first informal ballot, loses three positive votes and
gains three negative ones.
Otunnu shows the clearest improvement,
moving from 2 to 5 votes of support, while Bachelet suffers the sharpest fall,
dropping from 6 supporting votes to only 2. Grossi keeps his 7 votes of
support, but his discourage votes climb from 2 to 6; the stability of positive
votes therefore appears less relevant than the increase in aggregate
opposition.
This situation means that P5 uncertainty —
that is, the fact that we do not know whether any of the discourage votes came
from a permanent member of the Council, which would in practice amount to a
veto of a candidacy — increases for the two best-positioned candidates if we
count favorable votes: 73.6% for Rodrigues-Birkett and 84.6% for Grynspan,
according to the same model applied to the first straw poll.
|
Change in the
number of votes between the first two rounds |
|||||||||
|
Candidacy |
E1 |
E2 |
ΔE |
D1 |
D2 |
ΔD |
N1 |
N2 |
ΔN |
|
Carolyn Rodrigues-Birkett |
9 |
8 |
-1 |
2 |
3 |
+1 |
4 |
4 |
0 |
|
Rebeca Grynspan |
10 |
7 |
-3 |
1 |
4 |
+3 |
4 |
4 |
0 |
|
Rafael Mariano Grossi |
7 |
7 |
0 |
2 |
6 |
+4 |
6 |
2 |
-4 |
|
Macky Sall |
6 |
6 |
0 |
7 |
7 |
0 |
2 |
2 |
0 |
|
Olara Otunnu |
2 |
5 |
+3 |
5 |
5 |
0 |
8 |
5 |
-3 |
|
María Fernanda Espinosa |
5 |
4 |
-1 |
2 |
3 |
+1 |
8 |
8 |
0 |
|
Michelle Bachelet |
6 |
2 |
-4 |
5 |
6 |
+1 |
4 |
7 |
+3 |
Source:
Own
Let us briefly recall that the model I
propose recognizes that the person who manages to become United Nations
Secretary-General must meet two conditions: secure at least 9 votes in favor in
the Security Council and ensure that no permanent member votes against them.
This creates, in turn, a double uncertainty: uncertainty over the vote deficit
and uncertainty over possible vetoes.
Taking both elements into account, the
model calculates what we call “distance from the threshold” and “P5
uncertainty.”
|
|
Votes |
Distance from the threshold |
P5 Uncertainty |
|||||
|
Candidacy |
E |
D |
N |
Deficit |
Neutrals to convert |
Minimum D votes to reverse |
No P5 |
At least one P5 |
|
Carolyn Rodrigues-Birkett |
8 |
3 |
4 |
1 |
25% |
0 |
26,4% |
73,6% |
|
Rebeca Grynspan |
7 |
4 |
4 |
2 |
50% |
0 |
15,4% |
84,6% |
|
Rafael Mariano Grossi |
7 |
6 |
2 |
2 |
100% |
0 |
4,2% |
95,8% |
|
Macky Sall |
6 |
7 |
2 |
3 |
150% |
1 |
1,9% |
98,1% |
|
Olara Otunnu |
5 |
5 |
5 |
4 |
80% |
0 |
8,4% |
91,6% |
|
María Fernanda Espinosa |
4 |
3 |
8 |
5 |
62,5% |
0 |
26,4% |
73,6% |
|
Michelle Bachelet |
2 |
6 |
7 |
7 |
100% |
0 |
4,2% |
95,8% |
|
Ivonne A-Baki |
0 |
8 |
7 |
9 |
128,6% |
2 |
0,7% |
99,3% |
Source: Own
From this aggregate table, we can see that:
Carolyn Rodrigues-Birkett
She moves into the strongest position: she
needs to convert one of four neutral votes, but her three discourage votes
raise the uncertainty of at least one P5 vote to 73.6%.
Rebeca Grynspan
She needs two additional votes of support
and must convert half of her neutral votes, which represents a double setback:
she loses three votes of support and gains three discourage votes. Her P5
indicator rises to 84.6%.
Rafael Grossi
He maintains seven votes of support, but
would have to turn both of his neutral votes into positive ones, while also
facing P5 uncertainty of 95.8%.
Macky Sall
He is the only candidate to repeat the same
result in both rounds (6-7-2), which means that turning his neutral votes into
support would still not be enough: he needs to gain the support of at least one
of those who have discouraged his candidacy. The current number of discourage
votes gives him the second-highest P5 uncertainty, reaching 98.1%, behind only
A-Baki.
Olara Otunnu
His position shows strong momentum compared
with the first round, but still leaves him in a difficult situation, since he
would need to turn at least four of the five neutral votes he received into
support and face five discourage votes, which produces P5 uncertainty of 91.6%.
María Fernanda Espinosa
She faces the challenge of turning at least
5 of her 8 neutral votes into support, but because she has the lowest number of
discourage votes outside the top two positions, her P5 uncertainty stands at
73.6%, equal to that of Rodrigues-Birkett and lower than Grynspan’s.
Michelle Bachelet
She is in a difficult position that would
require turning her seven neutral votes into support. Although turning neutrals
into positive votes would be enough for her, without needing to convert
negative votes into positive ones, the high number of discourage votes results
in P5 uncertainty of 95.8%.
Ivonne A-Baki
Newly added to the race, she received no
support and, even if she turned her seven neutral votes into support, would
still need to reverse two discourage votes. She is also the candidate with the
most discourage votes (8), resulting in the highest P5 uncertainty: 99.3%.
What to watch in the next round
I believe there are five main elements to
watch in the third straw poll:
- Whether Rodrigues-Birkett can secure the ninth vote of support
without increasing her discourage votes.
- Whether Grynspan manages to reverse her decline or whether it
begins to look like a trend.
- If Grossi fails to reduce the opposition he generates, whether
he will begin to fall out of the race.
- How Ivonne A-Baki evolves.
- Whether differentiated ballots appear for permanent and
non-permanent members, which would reduce P5 uncertainty by turning it
into a certainty to be integrated into the final calculation, putting an
end to the combinatorial uncertainty created by the observed number of
discourage votes.
In general terms, the hardest question, and
perhaps the best proxy indicator of how negotiations among Council members are
unfolding, is whether the overall decline in support reflects a more strategic
round of informal voting or represents real fragmentation.
It will also be important to begin
interpreting “no opinion” votes, particularly by trying to understand whether
they represent a “reserve of early support” or, on the contrary, a delay before
expressing a discourage vote.
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