Why does disaster endanger to support the strongest?

Because he'll get any of the fines lost by the weakest. The bonus will be shared with the PiS. Just like that. There is no request for D’Hondt's calculations, which rewards the strongest. The failure of votes may be up to 7% of TD if it does not exceed the coalition threshold and 4% of the Left for which the threshold is lower. This is 11% of all votes – as in 2015. Given that the division between the PiS and the Confederate, on the 1 hand, and the 3 opposition groups today, is close to balance, it is 22% of our vote. all 5th of us can waste a voice in the most pointless way. The operation makes sense then – and only then – erstwhile KO cannibalizes the remaining letters in full and erstwhile all their supporters simply transfer votes to KO. And that won't happen for sure.

As for D’Hondt. Algorithm makes things much more complicated here. Many times and industriously (e.g. here – I recommend) I utilized to convert votes into mandates in different variants of distribution between e.g. 2 opposition letters starting against 1 list of PiS to show that the common list of 2 parties is worth at least 5% of voters' votes. That means that the common list of opposition may have up to 5% of the votes little than would have been collected by 2 opposition parties starting separately, and the effect of dividing mandates with D’Hondt's algorithm would be about the same (although in my method of counting it would be very riskyly unpredictable due to the deficiency of continuity of model behaviour). This in turn would mean that a strategy to support the strongest organization might make sense. He's gone. besides in a situation where no 1 falls under the threshold. Although knowing already requires any effort.

Let's see. It's hard, no tables of numbers.

The set of Kasprzak and Machowski in the separate tables below means 2 different ways of counting, which, unfortunately, must be explained. First of all, my calculations are full of business – it is apparent that the strategy of "supporting strong" works against me erstwhile I run from the weaker list. Dr Andrzej Machowski remains beyond this kind of suspicions – he organized and developed 2 major civic investigation commissioned by the Long Table Forum Foundation and advocated (me too) in favour of a common list of opposition. Today, he could defend the thought of "the only list" if he did not burn out his (and our citizens of Poland) project. And he does not do so, although he knows the effect of the "D’Hondt premium" with quite a few work and his own simulations.

I number the allocation of seats at first glance, as the State Electoral Commission does, straight applying the consequence to each of the 41 electoral districts differing between the number of mandates and following the procedure applied by PKW. So I presume that the result, for example, of 35% for the Law and Justice Service is repeated in each of these districts. This, of course, is not only not true, and this misrepresentation has a crucial impact on the result, which is not necessarily "average", since D'Hondt divides the mandates not in line with the results. In addition, there are districts – specified as Warsaw – where KO runs, although on average in the country it loses. This causes deviations much larger. Therefore, the results I give are not a measurement of forecast and can service alternatively only qualitative or even illustrative comparisons of the behaviour of the algorithm with different input data – i.e. with different layouts of lists or different schedules of votes between them.

Machowski's counting differently. He went to quite a few trouble, which I did not ask myself, and D’Hondt's algorithm containing the procedure of subsequent calculation steps utilized by PKW, and described here in another text changed it to a set of equations to calculate the expected consequence directly. It's not difficult, but alternatively complicated reasoning, which I will not repeat here, due to the fact that it's inactive a dense text (I mention curious to the origin text). Key to assessing the differences between the 2 methods of its presumption with values of expected deviations between districts. In the Machowski method, they consequence from the purely arithmetic differences between districts (various number of seats), but on the occasion there are besides possible deviations in the percentages of votes. The "Machowski sets" can so be considered as real forecasts in contrast to the "Kasprzak sets". And they behave differently – they are devoid of utmost nonlinearity of model behavior. In short, Machowski counts the score of the X-lot in specified a way that he adds or subtracts the mandates for each percent of its deviation from the 20% average, with an average of 5.625 mandates for 5 lists, e.g. 5.42 mandates for 4 lists, where the deviation is measured from the 25% average and the "base" mandates are not 92 and 115 – which is crucial for 1 of the tables depicting the entry into the threshold of 1 of these lists.

All right, let's see. Let us set up a set of input data, assuming – as a realistic and optimistic adequate – that the sum of the expected votes for the opposition is precisely equal to the sum of the votes of the Law and the Confederation. 4 years ago, we got more votes than the PiS, but little than the PiS and the Confederacy. Like then, our score is divided into 3 lists. The strong PiS then led at the score rate and thus won. Let's see what happens erstwhile today's expected war results of the 2 camps, the list of KOs leads at the expense of the opposition partners, for which the strategy of supporting the strongest is to be calculated.

Kasprzak set – output data:

	Mandates	% of mandates	% of votes	Mandates in proportion	D’Hondta premium
PiS	173	37.61%	35,00 %	161	12
KO	161	35,00 %	32.00%	147	14
Left	22	4.78%	8.00%	37	-15.
TD	41	8.91%	10,00 %	46	-5
Confederation	63	13.70%	15,00 %	69	-6

The sum of the opposition's seats is 224. As expected, a number at the actual perfect balance in the voices. The column ‘Mandates in proportion’ is simply a percent consequence multiplied by 460 seats in the Sejm and rounded to the nearest integer. The D’Hondt premium is simply a simple difference between this consequence and the actual lot allocated with the number of mandates.

Machowski set – output data:

	% of heads	Average %	Deviation %	Mandates on average	Mandates with bonus
PiS	35,00 %	20,00 %	15,00 %	92	176
KO	32.00%	20,00 %	12.00%	92	160
Left	8.00%	20,00 %	-12.00%	92	25
TD	10,00 %	20,00 %	- 10.00%	92	36
Confederation	15,00 %	20,00 %	-5.00%	92	64

The opposition gets a small little here due to the fact that 220 tickets. besides as expected. The Machowski model clearly shows that the "D’Hondt premium" is given to you with a percent of the vote above the 20% average and they lose those below that average. The consequence e.g. PiS – I will repeat the method described above – Machowski calculates according to expression 460/5 + (35 – 100/5) x 5,625, or 92 + 5,625 x 15.

"Let's spin the slider". The results of the Law and the Confederacy stay unchanged and we manipulate only the results of the opposition leaving the sum unchanged. Let KO take 5% of the left and TD votes, thus exceeding the PiS score and in the race for the bonus going to lead 37 to 35.

Kasprzak set:

	Mandates	%mandate	%voice	Mandates in proportion	D’Hondta premium
PiS	173	37.61%	35,00 %	161	12
KO	195	42.39%	37.00%	170	25
Left	1	0.22%	5,00 %	23	-22.
TD	27	5.87%	8.00%	37	-10.
Confederation	64	13.91%	15,00 %	69	-5

Well, 223 mandates – failure of mandate compared to the erstwhile consequence in this set, although KO gained very much. The not-linearly strong failure of the Left and the TD failure with the unchanged consequence surprises. The D’Hondt algorithm is in no way able to behave like this, and likewise unexpected behaviour comes especially from districts with a low number of mandates.

The Machowski set, which, with all its characteristics, the size of districts does not include, mitigates these behaviours:

	% of heads	Average %	Deviation %	Mandates on average	Mandates with bonus
PiS	35,00 %	20,00 %	15,00 %	92	176
KO	37.00%	20,00 %	17.0%	92	188
Left	5,00 %	20,00 %	-15.00%	92	8
TD	8.00%	20,00 %	-12.00%	92	25
Confederation	15,00 %	20,00 %	-5.00%	92	64

But the consequence surprises even more – 220 tickets, no change compared to the erstwhile set and little than my respect for the same data!

All of this takes place on the border of worse risk, due to the fact that both Left and TD are at the border of the electoral threshold. Let us do this, and in accordance with the wishes of “one-listers” let us drive the Holovnia with Kosiniak into the threshold they do not like.

Kasprzak set:

	Mandates	%mandate	%voice	Mandates in proportion	D’Hondta premium
PiS	190	41.30%	37.63%	173	17
KO	204	44.35%	40.86%	188	16
Left	2	0.43%	5.38%	25	-23.
TD	0	0,00 %	0,00 %	0	0
Confederation	64	13.91%	16.13%	74	-10.

206 opposition mandates and specified a turn of events were expected. The column % of the votes now shows 0 for TD, although in reality there is 7% there, but they do not number in D’Hondt's calculation, so unchanged in the absolute numbers of the PiS at pool division increased, as did all another non-zero results.

Machowski's set is somewhat little harsh:

	% of heads	Average %	Deviation %	Mandates on average	Mandates with bonus
PiS	37.63%	25,00 %	12.63%	115	183
KO	40.86%	25,00 %	15.86%	115	201
Left	5.38%	25,00 %	-19.62%	115	9
TD	0,00 %	25,00 %	-25.5%	115	-21.
Confederation	16.13%	25,00 %	-8.87%	115	67

The opposition has 210 tickets here. This is inactive the worst consequence of the options under consideration, dividing 50% of the opposition's support between 3 of its lists. crucial parameters of calculation have changed. The letters are now effectively 4, so the expected average score is 25%, and the average ticket pool to which we add a bonus and from which we deduct the punishment is now 460.4=115. The mysterious percent of seats for the percent of votes above the average has besides changed somewhat – now it is 5.42.

Which fundamentally ends the evidence. Dr. Machowski comments on the strategy of "supporting the strongest" – openly and bluntly:

"I believe that this is an highly dangerous game for us, and calling for specified migration (previously Markov had done so, but he understood his mistake, and now he urges Sadurski to do so) is highly irresponsible and shows a complete misunderstanding of D’Hondt's operation. And it besides seems that Tusk has now adopted specified a strategy.
As you can see, in the case of "eating" 1 organization (e.g. TD), as a result, which only 2 letters on our side participate in the division of mandates, this "eating" organization must be "eaten" in its entirety in order to be able to win a tie with the right.
In the case of "eating" 2 parties at erstwhile – i.e. erstwhile trying to make 1 list from the list of KOs – for Democrats with specified 1 list to win elections it is essential that KO take over over 3/4 of the erstwhile TD and Left voters. It's an impossible mission.
If – and I regret it – 1 list has not been made, it is crucial to guarantee that TD and Left do not fall under the threshold. And the KO should effort to get 1–2 p.p. of the Confederation better, due to the fact that without it it will be truly hard to win these elections.”

Exactly. Let's not let another madness happen after what politicians have already given us.