What are the advantages of list initialization (using curly braces)?

MyClass a1 {a};     // clearer and less error-prone than the other three
MyClass a2 = {a};
MyClass a3 = a;
MyClass a4(a);

Why?

Basically copying and pasting from Bjarne Stroustrup's "The C++ Programming Language 4th Edition":

List initialization does not allow narrowing (§iso.8.5.4). That is:

• An integer cannot be converted to another integer that cannot hold its value. For example, char to int is allowed, but not int to char.
• A floating-point value cannot be converted to another floating-point type that cannot hold its value. For example, float to double is allowed, but not double to float.
• A floating-point value cannot be converted to an integer type.
• An integer value cannot be converted to a floating-point type.

Example:

void fun(double val, int val2) {

    int x2 = val;    // if val == 7.9, x2 becomes 7 (bad)

    char c2 = val2;  // if val2 == 1025, c2 becomes 1 (bad)

    int x3 {val};    // error: possible truncation (good)

    char c3 {val2};  // error: possible narrowing (good)

    char c4 {24};    // OK: 24 can be represented exactly as a char (good)

    char c5 {264};   // error (assuming 8-bit chars): 264 cannot be 
                     // represented as a char (good)

    int x4 {2.0};    // error: no double to int value conversion (good)

}

The only situation where = is preferred over {} is when using auto keyword to get the type determined by the initializer.

Example:

auto z1 {99};   // z1 is an int
auto z2 = {99}; // z2 is std::initializer_list<int>
auto z3 = 99;   // z3 is an int

Conclusion

Prefer {} initialization over alternatives unless you have a strong reason not to.