socketio broadcast message only send to one

I am building a game using socketio.
The server stores the number of players, when it goes to 2, game start.
However, when I open two browser one by one, only the first one(not the latter one) receive the game start message.
Client side:

var socket = io.connect('http://localhost:8080');
socket.on('connected', function (data) {
    $('#status').html('You are connected');
    socket.emit('1 party connected');
});

socket.on('game start', function (data) {
    $('#status').html('game start');
});

Server side:

var app = require('http').createServer(handler)
  , io = require('socket.io').listen(app)
  , fs = require('fs')

app.listen(8080);

var connected_parties_no = 0;

io.sockets.on('connection', function (socket) {
  socket.emit('connected', { hello: 'world' });
  socket.on('1 party connected', function () {
    connected_parties_no++;
    console.log(connected_parties_no.toString()+' parties are connecting.');
    if (connected_parties_no == 2) {
      game_start(socket);
    }
  });
  socket.on('disconnect', function () {
    connected_parties_no--;
  });
});

function game_start(socket) {
  socket.broadcast.emit('game start');
}