Liberty of Indifference (liberum arbitrium indifferentiae) is for some philosophers an effort to identify "liberty" as merely some form of indeterminism or chance. This argument is popular with determinist and compatibilist philosophers who want to show that this kind of free will is not worth having.

For some philosophers of mind, it is an example of a mechanical equilibrium so finely balanced that even an immaterial mind could push the body in one direction or the other.

Liberty of Indifference was very popular among the Scholastics and is discussed extensively by rationalists like Descartes and Spinoza, and by empiricists like Locke, Berkeley, and Hume. It plays a large role in Schopenhauer's prize essay On the Freedom of the Will.

The metaphor of a balance is popular among philosophers whose model for mental actions is the resolution of forces like motives or desires. Is the will paralyzed when presented with identical choices? Of course there is no such thing as perfectly identical alternatives, but from ancient times philosophers argued this case, starting with Aristotle.

"there is this necessity of indifference...of the man who, though exceedingly hungry and thirsty, and both equally, yet being equidistant from food and drink, is therefore bound to stay where he is." (De Caelo, Book II, Sect.13, 295b31-33

Aristotle assumed it was obvious that the man would not starve. He used this argument as a sort of reductio ad absurdum. But later Scholastics took this argument very seriously, especially the logician Jean Buridan with his example of an ass placed equidistant between two identical bales of hay. Buridan used it to show a critical difference between man and animals.

The Scholastics claimed the ass would starve to death (which is nonsense), but a human in similar circumstances, with a god-given gift of free will (in this case the liberty of indifference) would deliberate and choose despite the perfect balance* between identical alternatives.

Liberty of Indifference was often contrasted with Liberty of Spontaneity, another name for the "negative freedom" when one is free from constraints. Liberty of Spontaneity was also called Voluntarism. For classical compatibilists like Hume, Voluntarism or Liberty of Spontaneity is compatible with determinism. Since the agent's will is in the causal chain of events, it is one of the causes and that is enough for compatibilist free will.

Liberty of Indifference, by contrast, was considered a positive freedom, first, to choose to act or not to act, and in more sophisticated libertarian positions, to choose from alternative actions.

Liberty of Indifference thus raises the question whether one could have done otherwise.

For David Hume, any liberty at all depends entirely on chance. Hume mistakenly generalized from the Liberty of Indifference where a random choice is quite rational between identical alternatives. He says that liberty is absurd and unintelligible, because it denies causality and necessity:

I believe we may assign the three following reasons for the prevalence of the doctrine of liberty, however absurd it may be in one sense, and unintelligible in any other. First, After we have perform'd any action; tho' we confess we were influenc'd by particular views and motives; 'tis difficult for us to persuade ourselves we were govern'd by necessity, and that 'twas utterly impossible for us to have acted otherwise; the idea of necessity seeming to imply something of force, and violence, and constraint, of which we are not sensible. Few are capable of distinguishing betwixt the liberty of spontaneity, as it is call'd in the schools, and the liberty of indifference; betwixt that which is oppos'd to violence, and that which means a negation of necessity and causes.
(Treatise on Human Nature, Book II, Part III, Sections I-II, p.407)

For Hume, liberty eliminates causality and necessity. The first compatibilist, Chrysippus, had settled for fate and determinism, while denying necessity. He agreed with Aristotle that necessity and freedom were incompatible.

The modern compatibilists, Hobbes and Hume, restored necessity to their compatibilism and began the trend among modern philosophers, especially those who favor Hume's naturalism, to call free will unintelligible.

Arthur Schopenhauer's essay "On the Freedom of the Will" won the prize of the Royal Danish Academy of Sciences in 1839. His description of his predecessors' work (pp. 65-90) is extensive. Schopenhauer defined absolute freedom - the liberum arbitrium indifferentiae - as not being determined by prior events. "Under given external conditions, two diametrically opposed actions are possible." He found this completely unacceptable.

If we do not accept the strict necessity of all that happens by means of a causal chain which connects all events without exception, but allow this chain to be broken in countless places by an absolute freedom, then all foreseeing of the future... becomes...absolutely impossible, and so inconceivable.

The future is of course not foreseeable, but chance is the direct cause of action only in those cases where no clear preference exists, the original and sound idea of a liberty of indifference. In those cases flipping a coin is an appropriate rational action. For all other cases, chance simply contributes creative alternative possibilities for the determined will to choose from with a much broader liberty than the restricted cases of indifference.

Kane has developed the idea of dual rational control in the case of a “torn decision,” (in which an agent has equally powerful reasons for choosing either way between two alternatives) and yet preserve the sense of moral responsibility. As long as the agent is prepared to accept responsibility either way, flipping a coin does no harm to moral responsibility.

Kane distinguishes such choices from the ancient Liberty of Indifference in which there is no meaningful differences between choices, such as the classic idea of Buridan's Ass.