Why a captured company doesn't un-capture itself: governance hysteresisPreco sa ovladnuta firma sama neuvolni: histereza v sprave firiem
The claim. There is a stake of committed shareholders or activists that flips a well-run company into a captured one. The surprise is that the stake needed to recover a captured company is not the samExistuje podiel akcionarov, ktory ovladne dobre vedenu firmu - a iny, mensi, ktory ju vrati spat. Nad kritickou mierou prepojenia vlastnictva podiel na navrat klesne na nulu: ovladnutie sa stane nezvratnym.
The claim. There is a stake of committed shareholders or activists that flips a well-run company into a captured one. The surprise is that the stake needed to recover a captured company is not the same - and above a critical level of board/owner coupling, it falls to zero. A captured firm then stays captured even if the capturing faction shrinks to nothing. Capture is path-dependent: you cannot undo it just by undoing its cause.
The measurement. We modeled a board/shareholder bloc as a coupled opinion system whose fundamentals favor good governance, and measured two thresholds: f_up, the committed stake that captures a firm starting in good control; and f_down, the stake below which a captured firm recovers on its own. As the coupling J rises:
| ownership coupling | capture stake (f_up) | recovery edge (f_down) | hysteresis |
|---|---|---|---|
| weak (J=1.2) | 14% | 14% | 0% - reversible |
| J=2.0 | 22% | 0% | 22% |
| J=3.0 | 28% | 0% | 28% |
| J=4.0 | 32% | 0% | 32% |
Below a critical coupling, capture is reversible (f_up = f_down). Above it, a hysteresis loop opens and widens: capturing costs more, while recovery by stake-reduction alone becomes impossible (f_down goes to 0).
The method, in two sentences. It is a mean-field Glauber model of a faction-versus-consensus tug-of-war, with a committed minority pinned at the capture position and a field representing fundamentals that favor good governance. We swept the coupling and, for each value, found the capture and recovery thresholds by starting respectively from the good-control and the already-captured state.
Why it matters. In highly-coupled ownership - proxy-advisor herding, common owners across an index, concentrated index funds - a captured firm entrenches far below the stake that captured it. Removing the activist does not restore good governance; recovery requires an active counter-force, not merely removing the cause. It is the same structure as a disease that does not reverse when you reverse the conditions, mapped onto corporate control.
The falsifierIf capture and recovery thresholds coincided at all couplings (no hysteresis), or if recovery were as easy as prevention in coupled boards, or if the loop did not widen with coupling, the claim would be empty. None of these held: the loop emerges above a critical coupling and widens with it.
What would change our mind. Real control-contest data in which recovered firms recovered at the same stake that captured them (no path-dependence), or in which high-coupling ownership showed easier - not harder - recovery. This is a model result; the next step is to test it against actual proxy-fight and entrenchment outcomes.
Tvrdenie. Existuje podiel odhodlanych akcionarov alebo aktivistov, ktory prevrati dobre vedenu firmu do ovladnuteho stavu. Prekvapenim je, ze podiel potrebny na navrat ovladnutej firmy nie je rovnaky - a nad kritickou mierou prepojenia predstavenstva/vlastnikov klesne na nulu. Ovladnuta firma potom zostane ovladnuta, aj keby sa ovladajuca skupina zmensila na nulu. Ovladnutie zavisi od cesty: neda sa zvratit len tym, ze odstranite jeho pricinu.
Meranie. Blok predstavenstva/akcionarov sme modelovali ako prepojeny system nazorov, ktoreho zaklady uprednostnuju dobre riadenie, a merali sme dva prahy: f_up - odhodlany podiel, ktory ovladne firmu zacinajucu v dobrom riadeni; a f_down - podiel, pod ktorym sa ovladnuta firma sama vrati. Ako rastie prepojenie J:
| prepojenie vlastnictva | podiel na ovladnutie (f_up) | hrana navratu (f_down) | histereza |
|---|---|---|---|
| slabe (J=1.2) | 14% | 14% | 0% - zvratne |
| J=2.0 | 22% | 0% | 22% |
| J=3.0 | 28% | 0% | 28% |
| J=4.0 | 32% | 0% | 32% |
Pod kritickym prepojenim je ovladnutie zvratne (f_up = f_down). Nad nim sa otvara slucka hysterezy a rozsiruje sa: ovladnutie stoji viac, kym navrat samotnym znizenim podielu sa stava nemoznym (f_down ide na 0).
Metoda v dvoch vetach. Je to mean-field Glauberov model preetahovania medzi frakciou a konsenzom, s odhodlanou mensinou ukotvenou na pozicii ovladnutia a polom, ktore predstavuje zaklady uprednostnujuce dobre riadenie. Prebehli sme rozsah prepojenia a pre kazdu hodnotu sme nasli prahy ovladnutia a navratu tak, ze sme zacali z dobreho riadenia, resp. z uz ovladnuteho stavu.
Preco na tom zalezi. Pri silne prepojenom vlastnictve - stadovanie proxy poradcov, spolocni vlastnici napriec indexom, koncentrovane indexove fondy - sa ovladnuta firma zakope hlboko pod podielom, ktory ju ovladol. Odstranenie aktivistu neobnovi dobre riadenie; navrat si vyzaduje aktivnu protisilu, nie len odstranenie priciny. Je to ta ista struktura ako choroba, ktora sa nezvrati, ked zvratite podmienky, prenesena na kontrolu nad firmou.
Falzifikator. Ak by sa prahy ovladnutia a navratu zhodovali pri vsetkych prepojeniach (ziadna histereza), alebo ak by navrat bol rovnako lahky ako prevencia v prepojenych predstavenstvach, alebo ak by sa slucka nerozsirovala s prepojenim, tvrdenie by bolo prazdne. Nic z toho neplatilo: slucka sa objavuje nad kritickym prepojenim a s nim sa rozsiruje.
Co by nas presvedcilo o opaku. Realne data z bojov o kontrolu, kde sa vratene firmy vratili pri rovnakom podiele, ktory ich ovladol (ziadna zavislost od cesty), alebo kde silne prepojene vlastnictvo vykazalo lahsi - nie tazsi - navrat. Toto je vysledok modelu; dalsim krokom je overit ho voci skutocnym vysledkom proxy bojov a zakopania sa.