This is a controversial topic (as you can imagine). Famines, genocides and other atrocities have happened in numerous places under numerous different economic and governing systems, including market democracies. Yet people generally don't look at say slavery in the USA, or the stolen generations of indigenous people in Canada and Australia, or settlers' seizure of Maori land in my own NZ, and conclude we should do away with democracy. Instead the hope is to reform and improve democracy, so we can have the good stuff (e.g. peaceful transitions of power) without the bad stuff. History gives us some reason for guarded optimisim on this point. I've been deliberately talking about democracy here on the basis that nearly everyone reading this will be in favour of democracy, but these considerations also apply to economic systems: one can acknowledge the harms that happened under market economies, or centrally-planned economies, and hope to improve things so these no longer happen within the existing framework. Including by better means of choosing who holds positions of power. 

Institutions do matter

This is not to say that every atrocity is down to the choices of individuals actions of certain people in positions of power. The Economics Nobel Laureate, Amartya Sen, in 1981 argued that famines don't occur in democracies with an independent press, and further testing of this hypothesis has generally supported it (Burchi, 2011). 

And there is a theoretical argument that centrally-planned economies have tendencies within them that will lead to totalitarianism. This was famously, and controversially, made by Frederick Hayek in his 1944 book The Road to Serfdom. Hayek's argument was that implementing central planning requires that planners act according to a scale of values, and any set of values are vanishingly unlikely to command unanimous agreement. To explain a bit further, economies are highly interlinked: for example railways use steel, much machinery uses steel, steel-making uses iron ore, ore mining uses machinery, and that machinery uses steel. Therefore, if the decision is made to extend the railway system this will have consequences: should the supply of machinery be cut? And if so, what types? Should for example fewer telephones be made? Or fewer shovels? Can some machines be made using less steel, and if so what else will they demand more of? Should the supply of steel be increased? If so then iron ore mining must expand. And these decisions extend through time: a decision to expand the manufacture of mining machines so as to mine more iron ore so as to make more steel can mean cutting consumption today. In a market economy, these flow-on impacts are mediated (imperfectly) by prices: if more people want to use steel then the price rises, and these higher prices induce other people to see if they can cut back their use, or start supplying more steel. If the demand for steel is expected to rise for an extended period of time, people can make their own decisions as to whether to invest more now, or maintain their consumption. Under central planning, these decisions have to be made by the planners. There is no one right answer, instead a set of values might be chosen. And not just a loose value like "invest now for the future", but a very detailed set, that goes down to questions like "do we value making a thousand spades available for gardeners working in public parks more or less than building an indoor public swimming pool with a slightly safer steel frame in an earthquake prone area?"  (This specific example is mine, not Hayek's).

Clearly these tradeoffs are questions people would struggle to agree on, and we can think of more controversial topics than public gardens versus swimming pools where people might have very strong disagreements. But a plan is only workable if people carry it out: if the steel needed to build the railways is instead diverted to shovels by fervent lovers of public parks, then the steel is lost from somewhere else (and since gardeners need more than shovels, there's other flow on impacts). So planners must not only make decisions based on values shared by only a few, but also get everyone else to go along with said decisions: by propaganda or by force. This is incompatible with democracy and individual rights, including an independent press. 

So, if Hayek's argument is correct, then, given the association that Amartya Sen noted between democracy, independent press, and an absence of famines, it therefore follows that centrally-planned economies would be systematically prone to abuses by individual actions of certain people in positions of power. Hayek also argues that central planning will tend to result in a bias towards a certain type of person getting into power who would also be more prone to carry out atrocities - someone who is confident in their own beliefs about what values are right and who is willing to override the opinions of others in order to get things done.  

In defence of Hayek

This thesis is controversial, and the two times I've cited Hayek on r/askhistorians, I've garnered a response that Hayek is a crank, not worthy of consideration, including once by a flaired member who has written a number of very high quality, well-researched comments. Unfortunately neither comment included any source for their assertion, so I can't assess the criticism on its own merits. In the hope of provoking a bit more detailed response this time, I'll say that to the best of my knowledge, generally Hayek is regarded on a similar level to other prominent economists by economists and economic historians, so as someone to be refered to, agreed with on some points, and disagreed on others. To give some sources, when The Road to Serfdom was first published, John Maynard Keynes wrote a letter praising it in general, while disagreeing on some points (Christainsen, 1993). Even the socialist economist Evan Durbin called Hayek's work "sincere, eloquent and influential", while still disagreeing with it (Durbin, 1945).

In this century, in 2017, the Keynesian and economic historian Brad De Long gave a characteristically complex opinion on Hayek on his blog. Gregory Mankiw, the  Robert M. Beren Professor of Economics at Harvard University, and a self-described Keynesian and Friedmanite also praised Hayek (and Galbraith) in his blog in 2006 (yes, only praised. Mankiw is extraordinarily nice for an economist.) And the economic historian Bruce Caldwell published an annoted edition of The Road to Serfdom in 2007, which was reviewed for EH.net (the Economic History Association's website) without any mention of crankiness on the part of Hayek. 

I suspect that the commentators may have been thinking of common mainstream economists' views of Austrian Economics and attributing this view to Hayek on the very logical basis that Hayek was actually Austrian. But there are some important distinctions there as Bryan Caplan argues in Why I am Not An Austrian Economist. It is of course possible that economists are wrong in these views, there are some rather more critical views, see Farrant and McPhail (2011), and I am happy to enter into a longer discusson on this point.