Ask Lemmygrad

Although people here have provided fantastic resources, I think the question may need to be approached a bit differently.

Intent is immediately relavent.

For one, if you're going to argue someone, it's important to know if this person is an associate, friend, colleague, or stranger, and if they are even open to changing their mind in the span of a single conversation. If they aren't, then it's not really worth arguing beyond the benifet of any on lookers or to simply plant seeds that hopefully sprout later.

With that said, and assuming you're talkng to someone in goid faith, the next thing I think it's important to understand is:

why is this person arguing with me?

A lot of the time, when people assert that western liberal democracy is more democratic than Marxism-Leninism, they aren't actually concerned with the debate about which structure of governance better facilitates rule by the people. What they are often doing is challenging the idea that ML states will work to their benifet and not restrict them unnecessarily. They see how Western liberal democracy does not restrict their ability to complain but nothing gets done, and they are fearful that if an ML state works against their benifet, then it'll leave them with less then they had before.

It's why they usually use hypotheticals to explain their point or ask questions. They don't fundamentally understand that an ML state is structured in a way that privileges them as workers.

You have to be able to expand the other persons view of how they participate in soceity

So as well as explaining how the Vanguard party works in a place like China, Cuba, Vietnam, etc, (which comrades here have provided resources on) it's important to discuss other areas of popular control in these projects.

For example, in China, every large enterprise has a union and worker council attached to it. This means that your average worker doesn't just have representation in their local political scene, but at their workplace as well.

It's also good, in my opinion, to explain how Chinese state ownership of large industries actually works. As in, it's a gradual level of nationalization where as an industry expands, higher levels of governance from local to national, link that industry to the communities they represent.

Lastly, it's good to just bring up the fact that ML states consistently follows the will of its people. China especially, due to its largely unrestricted access to the global economy, consistently makes decisions that benifet its people when it has every oppurtnity not to, like the US. At some point it just becomes ludicrous to believe that a country's leadership is able to male the correct decisions 99% of the time without any input of its populace.

Democracy can only really be measured by how effectively it achieves the needs, representation and approval for those it represents. Western liberal democracies don't do this. They are only democratic from the perspective of capitlists.