This is an announcement for the paper "On left democracy function" by P. Wojtaszczyk. Abstract: We continue the study undertaken in \cite{GHN} of left democracy function $h_l(N)=\inf_{\#\Lambda=N}\left\|\sum_{n\in \Lambda_N} x_n\right\| $ of an unconditional basis in a Banach space $X$. We provide an example of a basis with $h_l$ non-doubling. Then we show that for bases with non-doubling $h_l$ the greedy projection is not optimal. Together with results from \cite{GHN} and improved by C. Cabrelli, G. Garrig\'os, E. Hernandez and U. Molter we get that the basis is greedy if and only if the greedy projection is optimal. Archive classification: math.FA Submitted from: wojtaszczyk@mimuw.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.4972 or http://arXiv.org/abs/1303.4972