[click here to read "What 'Equality' Does NOT Mean"]
EGALITARIANISM AND PRIVATE PROPERTY
[Also see "Luxuries and Egalitarianism"]
Yes, people own private property in an egalitarian society. The egalitarian principle of "From each according to ability, to each according to need" (which is short for "From each according to reasonable ability, to each according to reasonable need or desire, with scarce things rationed equitably according to need") is perfectly consistent with, and in agreement with, people owning private property.
What distinguishes private property ownership in an egalitarian society from private property ownership in a non-egalitarian society based on class inequality (such as our present capitalist one) is this: in an egalitarian society egalitarians--those who support the principle of "From each according to ability, to each according to need," who are the vast majority of people in most communities--democratically decide in their local assembly which claims to private property ownership are reasonable and which are not.
The private property that most ordinary people own today--their house (if they're lucky enough to actually own it!), the land their house and back yard or garden are on, the things that are inside their house (and garage if they're lucky enough to have one), a small boat (again, if they're lucky enough to have one), etc.--would most likely be considered by the egalitarians in their community's local assembly to be reasonably owned as private property. Why?
Because these are things that an individual (or family), by themselves, make proper and reasonable personal use of. Also, things that an individual (or family) create with ONLY their own labor (or with tools and machines and raw materials obtained in trade for things made only with their own labor) would most likely be considered by the local assembly of egalitarians to be reasonably owned by the individual (or family) as their private property. Also, things that are of sentimental value to a particular person but not otherwise of great value would likely be considered reasonably owned by the individual for whom they are of sentimental value.
Things, and only things, that are reasonable for an individual or family to own* as private property are also reasonable for them to inherit as private property.
Some things, however, would likely NOT be considered reasonable to be owned as the private property of a single individual or small group of people, and would be considered instead to be under the control of the local assembly. What kind of things are we talking about? Things like this:
A large tract of land that should reasonably be enjoyed by lots of people for recreation
Natural resources needed by many people
The "air waves" for communication
Streets for transportation
A large tract of land that is suitable for agriculture and which would require the labor of very many people
Things or places where many people work, such as a factory, warehouse, skyscraper, office building, mine, hospital or university
Things the production of which requires the labor, directly or indirectly, of many people, essentially of society (such as highways and railroads)
Other similar things that an individual or family does not, by themselves, make proper and reasonable personal use of, such as multiple mansions or homes in which other people or families live, or a home in which nobody lives.
What about luxury items, such as a huge yacht, a personal jet, extremely valuable artwork, and so forth? Local assemblies will have to decide on a case-by-case basis. The guiding principle is that scarce things should be equitably rationed according to need, and if nobody really needs something but many desire it, then it can be rationed with something like a lottery. There could also be a time limit on how long somebody owns something, such as a piece of artwork or a yacht--whatever egalitarians in the local assembly decide is reasonable.
In some parts of the world, including the United States, there is a long tradition that defines freedom as the right to own private property. Egalitarianism is in agreement with this tradition in so far as this tradition is stated as the "right to own private property reasonably"--with "reasonably" defined as above and determined in specific cases by the local assembly of egalitarians in the relevant community.
There is, however, a big difference between the "right of reasonable private property" versus the "right of private property." For example, the American Revolution** took property away--without compensation--from some people who claimed (with perfectly "legal" documents) to own extremely unreasonable amounts of land. "The largest estate confiscation in all colonies was that of the Penn family, which at 21.5 million acres was worth a million pounds. Under the Divesting Act of 1779, Pennsylvania's Assembly took control of these vast holdings of the proprietor's family [the Penn family.] Virginia confiscated the six-million-acre Fairfax estate. In Massachusetts, a law was passed confiscating the property of everyone who had fought against the colonies; the aristocratic William Pepperel lost his lands, which stretched for thirty miles along the coast of Maine (then part of Massachusetts)...Nor did the provincial and state committees and governments simply resell confiscated lands to wealthy bourgeois...By and large, in what amounted to a virtual land redistribution, the broken-up estates were sold in small parcels to ordinary farmers and agricultural workers. To sell tracts of land in excess of 500 acres was viewed with opprobrium." [from The Third Revolution, vol. 1, pg. 222, by Murray Bookchin]
Anti-egalitarians defend class inequality by arguing that "The right to private property is sacred, and the basis for freedom." Egalitarians know that this is a specious argument that only sounds true when people forget about the huge difference between "reasonable private property" and "unreasonable private property."
There were conflicting aims by opposing groups of people inside the American Revolution. Many of the revolutionaries had egalitarian values and aims, but these values and aims were not stated explicitly, at least not nearly as often and as effectively as the contrary values and aims espoused and advocated by the upper class that came to dominate post-revolutionary American society and create what became the thoroughly capitalist society of class inequality that exists today. This underscores the crucial importance of building an explicitly egalitarian revolutionary movement.
* A person may "have" but not "own" something. For example, some scarce things such as luxuries like a yacht or a Rolex watch that nobody needs would be equitably rationed as discussed here. When somebody receives such an item--possibly by winning a lottery--they "have" it for some specified period of time but they don't "own" it; they cannot bequeath it to an heir the way they could an item of sentimental value that they owned. The Local Assembly of Egalitarians is the final authority in such matters, determining what is reasonable or not to be inherited in accordance with the egalitarian principle regarding wealth: "From each according to reasonable ability, to each according to need or reasonable desire with scarce things equitably rationed according to need." The Local Assembly should base its decisions, as much as possible, on formal explicit policies determined by and made public by the Local Assembly, and not on arbitrary whim or prejudice. The aim is to enable people to enjoy private property without enabling great wealth (and hence power) to become concentrated in the hands of a few.
** As I discuss in "The U.S. 'Founding Fathers' Were Enemies of 'We the People'," ordinary people who fought in (on the side of) the American Revolution did so to make society more equal, whereas the top leaders such as George Washington only pretended to have this goal and actually betrayed this aim of the revolution.