Why can't I compile an unordered_map with a pair as key?

You need to provide a suitable hash function for your key type. A simple example:

#include <unordered_map>
#include <functional>
#include <string>
#include <utility>

// Only for pairs of std::hash-able types for simplicity.
// You can of course template this struct to allow other hash functions
struct pair_hash {
    template <class T1, class T2>
    std::size_t operator () (const std::pair<T1,T2> &p) const {
        auto h1 = std::hash<T1>{}(p.first);
        auto h2 = std::hash<T2>{}(p.second);

        // Mainly for demonstration purposes, i.e. works but is overly simple
        // In the real world, use sth. like boost.hash_combine
        return h1 ^ h2;  
    }
};

using Vote = std::pair<std::string, std::string>;
using Unordered_map = std::unordered_map<Vote, int, pair_hash>;

int main() {
    Unordered_map um;
}

This will work, but not have the best hash-properties^†. You might want to have a look at something like boost.hash_combine for higher quality results when combining the hashes.

For real world use: Boost also provides the function set hash_value which already provides a hash function for std::pair, as well as std::tuple and most standard containers.

---

^†More precisely, it will produce too many collisions. E.g., every symmetric pair will hash to 0 and pairs that differ only by permutation will have the same hash. This is probably fine for your programming exercise, but might seriously hurt performance of real world code.

My preferred way of solving this problem is to define a key function that transforms your pair into a unique integer (or any hashable data type). This key is not the hash key. It is the unique ID of the pair of data that will then be optimally hashed by the unordered_map. For example, you wanted to define an unordered_map of the type

  unordered_map<pair<int,int>,double> Map;

And you want to use Map[make_pair(i,j)]=value or Map.find(make_pair(i,j)) to operate on the map. Then you'll have to tell the system how to hash a pair of integers make_pair(i,j). Instead of that, we can define

  inline size_t key(int i,int j) {return (size_t) i << 32 | (unsigned int) j;}

and then change the type of the map to

  unordered_map<size_t,double> Map;

We can now use Map[key(i,j)]=value or Map.find(key(i,j)) to operate on the map. Every make_pair now becomes calling the inline key function.

This method guarantees that the key will be optimally hashed, because now the hashing part is done by the system, which will always choose the internal hash table size to be prime to make sure every bucket is equally likely. But you have to make yourself 100% sure that the key is unique for every pair, i.e., no two distinct pairs can have the same key, or there can be very difficult bugs to find.

For pair key, we can use boost pair hash function:

#include <iostream>
#include <boost/functional/hash.hpp>
#include <unordered_map>
using namespace std;

int main() {
  unordered_map<pair<string, string>, int, boost::hash<pair<string, string>>> m;

  m[make_pair("123", "456")] = 1;
  cout << m[make_pair("123", "456")] << endl;
  return 0;
}

Similarly we can use boost hash for vectors,

#include <iostream>
#include <boost/functional/hash.hpp>
#include <unordered_map>
#include <vector>
using namespace std;

int main() {
  unordered_map<vector<string>, int, boost::hash<vector<string>>> m;
  vector<string> a({"123", "456"});

  m[a] = 1;
  cout << m[a] << endl;
  return 0;
}