Jakob Hruby Registers Classifications and Geoinformation Division Neuchtel
Jakob Hruby Registers, Classifications and Geoinformation Division Neuchâtel September 2018 www. statistik. at An Iterative Enterprise Group Algorithm
The Data Raw data about enterprises and people related to them - Shareholders - Owners - Operatives - … For each type of legal entity we have to define the amount of control this role leads to. www. statistik. at Slide 2 | September 2018
The Data This results in direct relations between legal units as „children“ and legal units or people as „parents“: www. statistik. at Child Parent Share Example LLC John Doe 20% Example LLC Shareholders United LLC 80% Sample LP Samantha Sample 100% … … … Slide 3 | September 2018
Objective Interconnect the one-to-one-relations, so that they form networks of relations, i. e. Enterprise Groups. What criterion is necessary for an enterprise to belong to a group? Definition of „Control“ www. statistik. at Slide 4 | September 2018
Direct Control A parent holds direct control of an enterprise if it holds more than 50% of its shares. A Parent A holds direct control of B. 70% B www. statistik. at No other parent can have direct control. Slide 5 | September 2018
Indirect Control A parent holds indirect control of an enterprise if the sum of all shares it controls directly or indirectly exceed 50%. A 100% 60% C D 15% 40% B www. statistik. at A holds indirect control of B, but A is not necessarily directly related to B. A single parent may or may not hold direct control of B. Slide 6 | September 2018
Indirect Control 1) Indirect Control comprises direct control 2) Indirect Control is defined recursively. We need criteria for our data: a) finite networks b) Uppest shares are directly controlled c) No circular relations www. statistik. at Slide 7 | September 2018
Indirect Control The criteria a) and b) are fulfilled by the simple fact, that we are dealing with finite datasets. The criterion c) is troublesome. Therefore: • Prevent/eliminate circular relations from the data beforhand or • Change the definition of control to explicitely deal with circular relations www. statistik. at Slide 8 | September 2018
Recursive Algorithm Question: How to find out who controls A? 33% 33% A From the recursive control criterion it is simple to intuitively build a recursive algorithm to determine control for a single enterprise. www. statistik. at Slide 9 | September 2018
Recursive Algorithm A www. statistik. at Slide 10 | September 2018
Recursive Algorithm B J L A www. statistik. at Slide 11 | September 2018
Recursive Algorithm C D B E J L A www. statistik. at Slide 12 | September 2018
Recursive Algorithm C D B E J L A www. statistik. at Slide 13 | September 2018
Recursive Algorithm F C D B E J L A www. statistik. at Slide 14 | September 2018
Recursive Algorithm G F C D B E J L A www. statistik. at Slide 15 | September 2018
Recursive Algorithm H I G F C D B E J L A www. statistik. at Slide 16 | September 2018
Recursive Algorithm H I G F C D B E J L A www. statistik. at Slide 17 | September 2018
Recursive Algorithm H I G F C D B E J L A www. statistik. at Slide 18 | September 2018
Recursive Algorithm H I G C F C D E B J L A www. statistik. at Slide 19 | September 2018
Recursive Algorithm H I G C F C D E B J L A www. statistik. at Slide 20 | September 2018
Recursive Algorithm H I G C F C D E B K J L A www. statistik. at Slide 21 | September 2018
Recursive Algorithm H I G C F C D E B K J L A www. statistik. at Slide 22 | September 2018
Recursive Algorithm H I G C F C D E B K J L A www. statistik. at Slide 23 | September 2018
Recursive Algorithm H I G C F C D E B K J C M N L A www. statistik. at Slide 24 | September 2018
Recursive Algorithm H I G C F C D E B K J C M N L A www. statistik. at Slide 25 | September 2018
Recursive Algorithm H I G C F C D E B K K J C M N L A www. statistik. at Slide 26 | September 2018
Recursive Algorithm H I G C F C D E B K K J C M N L A www. statistik. at Slide 27 | September 2018
Recursive Algorithm H I G C F C D E B K J C K M M N L A www. statistik. at Slide 28 | September 2018
Recursive Algorithm H I G C K F C D E B K J C K M M N L A www. statistik. at Slide 29 | September 2018
Recursive Algorithm H I G C K F C D E B K J C K M M N L A www. statistik. at Slide 30 | September 2018
Recursive Algorithm C controls B with 66% shares and therefore controls Bs share of 33% on A. K controls J with 100% and K controls L with 66% and therefore controls 66% shares on A. K controls A H I G C K F C D E B K J C K M M N L A www. statistik. at Slide 31 | September 2018
Recursive Algorithm Problems with this approach: Calculates the same information multiple times Fix: Caching information, still requires extra storage and runtime Instability in long networks, because the program opens itself over and over again. Circular relations cannot be dealt with Fix: Use a blacklist of members, that have been jumped to and must not be jumped to again www. statistik. at Slide 32 | September 2018
Iterative Algorithm Assume we already knew of subgroups, of the kind that sticks together: B A 51% F 100% D 45% C J 90% E 45% H G 75% 100% Question: How to determine into which subgroup to put another member and how to interconnect them? www. statistik. at Slide 33 | September 2018
Iterative Algorithm Answer: When the sum of direct relations into a single subgroup exceeds 50%. Example: B A 51% 45% F 100% D 45% C 20% 10% 25% X J 90% E 45% H G 45% 75% 100% 55% Y X belongs to F and Y belongs to J www. statistik. at Slide 34 | September 2018
Iterative Algorithm Start: Determine all natural subgroups • All direct relations with >50% shares Iteration: • For all enterprises determine whether they belong to a subgroup (sum >50%) • Add them and all enterprises of their subgroup (if they have one) to that subgroup • repeat www. statistik. at Slide 35 | September 2018
Iterative Algorithm Start F M D N G F H L K C A E I K M J B www. statistik. at Slide 36 | September 2018
Iterative Algorithm Step 1: F M D Add to subgroup G F N H L C A >50% E K J I Add to subgroup K M B www. statistik. at Slide 37 | September 2018
Iterative Algorithm Step 2: G F H L D C A www. statistik. at I >50% K E M B N J Slide 38 | September 2018
Iterative Algorithm Step 3: G F H I D K C A E B www. statistik. at >50% M N J L Slide 39 | September 2018
Iterative Algorithm Step 4: No more changes possible, algorithm terminates G F H I D www. statistik. at C K E M B N A J L Slide 40 | September 2018
Iterative Algorithm Step 4: No more changes possible, algorithm terminates G F H I D www. statistik. at C K E M B N A J L Slide 41 | September 2018
Iterative Algorithm Advantages: • Shorter runtime for big amounts of data; all groups calculated simultaneously • No recursive instability • Circular relations are no big problem (may require an extra termination rule) Disadvantage: • Needs to run on all data at once, no calculation for only a single enterprise possible www. statistik. at Slide 42 | September 2018
Contact information: Jakob Hruby Guglgasse 13, 1110 Vienna Tel: +43 (1) 71128 -8128 Jakob. Hruby@statistik. gv. at www. statistik. at An Iterative Enterprise Group Algorithm Slide 43 | September 2018
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